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Karachik, Valeriy Valentinovich

Total publications: 106 (93)
in MathSciNet: 58 (58)
in zbMATH: 57 (50)
in Web of Science: 42 (42)
in Scopus: 49 (49)
Cited articles: 65
Citations in Math-Net.Ru: 291
Citations in Web of Science: 271
Citations in Scopus: 374
Presentations: 1

Number of views:
This page:6189
Abstract pages:14298
Full texts:3937
References:2061
Senior Researcher
Doctor of physico-mathematical sciences (2001)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
Keywords: partial differential equations, boundary value problems, polynomial solutions, polyharmonic functions, Greens function, special polynomials and functions.
UDC: 517.956.22, 517.956, 517.956.225, 517.572, 517.575
MSC: 35C05, 35C10, 35C11, 35J05, 35J40, 31B30, 11B37

Subject:

Representations of solutions to boundary value problems for partial differential equations: solutions in closed form, series solutions, integral representations of solutions.

Biography

1977 — graduated with honor from Tashkent State University.
1977–1978 — engineer, Institute of Cybernetics of Academy of Sciences of Uzbekistan;
1988 — Candidates degree, Institute of Mathematics of Academy of Sciences of Uzbekistan;
1991 — academic rank Senior Researcher;
1996 — Head of a Department, Institute of Cybernetics;
1996–1999 — Senior Researcher, University of World Economy and Diplomacy (UWED), Tashkent;
2000–2003 — Director of Computerized Testing Center, UWED;
2001 — Doctorates degree, Institute of Mathematics of Academy of Sciences of Uzbekistan;
2004–2011 — Professor, Department of Mathematical Analysis, South Ural State University, Chelyabinsk, Russia;
2011–2012 — Head of the Department of Differential Equations and Dynamical Systems, SUSU;
2013 — Head of the Department of Mathematical Analysis, SUSU;
09.2013 — Professor, Department of Mathematical and Functional Analysis, SUSU;

Member of American Mathematical Society (1997) and European Mathematical Society; Reviewer of Mathematical Reviews (1997), Zentralblatt fur Mathematik (1992).

   
Main publications:
  1. V. V. Karachik, “A problem for the polyharmonic equation in the sphere”, Siberian Mathematical Journal, 32:5 (1991), 767774  crossref  scopus
  2. V. V. Karachik, “Polynomial solutions to the systems of partial differential equations with constant coefficients”, Yokohama Math. J., 47 (2000), 121142  mathscinet
  3. V. V. Karachik, Method of normalized systems of functions, Publishing Center of SUSU, Chelyabinsk, 2014  zmath
  4. V. V. Karachik, “Construction of Polynomial Solutions to the Dirichlet Problem for the Polyharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 54:7 (2014), 11221143  crossref  adsnasa  isi
  5. V. V. Karachik, “On the Arithmetic Triangle Arising from the Solvability Conditions for the Neumann Problem”, Math. Notes, 96:2 (2014), 217227  crossref  isi

http://www.mathnet.ru/eng/person28783
https://scholar.google.com/citations?user=HPhjUpoAAAAJ&hl=en
https://zbmath.org/authors/?q=ai:karachik.valery-v
https://mathscinet.ams.org/mathscinet/MRAuthorID/248313
https://elibrary.ru/author_items.asp?spin=7397-3067
ISTINA http://istina.msu.ru/workers/134244389
http://orcid.org/0000-0002-3077-3595
http://www.researcherid.com/rid/J-6880-2016
https://www.scopus.com/authid/detail.url?authorId=6602898763
https://www.researchgate.net/profile/Valery_Karachik

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |


1. V. V. Karachik, Mat. Zametki (to appear)  mathnet

   2021
2. V. V. Karachik, “Greens functions of some boundary value problems for the biharmonic equation”, Complex Variables and Elliptic Equations, 2021 (Published online)  crossref  isi  scopus
3. B. Kh. Turmetov, V. V. Karachik, “O zadache Dirikhle dlya nelokalnogo poligarmonicheskogo uravneniya”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Matematika. Mekhanika. Fizika., 13:2 (2021), 37–45  crossref  elib
4. V. V. Karachik, “Greens Functions of the Navier and RiquierNeumann Problems for the Biharmonic Equation in the Ball”, Differential Equations, 57:5 (2021), 654–668 https://link.springer.com/article/10.1134/S0012266121050098  crossref  crossref  elib
5. Sh.A. Alimov, R.R. Ashurov, T.Sh. Kalmenov, B.E. Kanguzhin, V.V. Karachik, M.A. Sadybekov, A.M. Sarsenbi, D. Suragan, N.E. Tokmagambetov, B.T. Torebek, S.R. Umarov, V.E.Fedorov, “Batyrkhan Khudaibergenovich Turmetov (k 60-letiyu so dnya rozhdeniya)”, Chelyabinskii fiziko-matematicheskii zhurnal, 6:1 (2021), 5–9 http://cpmj.csu.ru/index.php/cpmj/issue/view/22  mathnet  elib

   2020
6. V. Karachik, B. Turmetov, “Solvability of one nonlocal Dirichlet problem for the Poisson equation”, Novi Sad Journal of Mathematics, 50:1 (2020), 67–88 https://www.dmi.uns.ac.rs/nsjom/paper.html?noid=ns8942  crossref  scopus
7. V. V. Karachik, “The Green Function of the Dirichlet Problem for the Triharmonic Equation in the Ball”, Mathematical Notes, 107:1 (2020), 105–120  mathnet  mathnet  crossref  crossref  mathscinet  mathscinet  zmath  isi  elib  scopus (cited: 2)
8. V. V. Karachik, “Class of Neumann-Type Problems for the Polyharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 60:1 (2020), 144162  mathnet  crossref  crossref  crossref  mathscinet  adsnasa  isi (cited: 1)  elib  scopus (cited: 1)
9. V. Karachik, B. Turmetov, “On solvability of some nonlocal boundary value problems for biharmonic equation”, Mathematica Slovaca, 70:2 (2020), 329–342  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1)
10. V. V. Karachik, “Usloviya razreshimosti zadachi Neimana $N_2$ dlya poligarmonicheskogo uravneniya v share”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Matematika. Mekhanika. Fizika., 12:2 (2020), 13–20  mathnet  crossref  mathscinet  elib
11. V. V. Karachik, “Neumann type problems for the polyharmonic equation in ball”, Journal of Mathematical Sciences, 249:6 (2020), 974–988 https://rdcu.be/b6vMJ  crossref  mathscinet  zmath  scopus
12. V. V. Karachik, “Predstavlenie resheniya zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share cherez funktsiyu Grina”, Chelyabinskii fiziko-matematicheskii zhurnal, 5:4-1 (2020), 391399  mathnet  crossref  scopus
13. V. V. Karachik, Integraly Rimana i Lebega, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2020 , 205 pp.  elib

   2019
14. V. Karachik, “Greens function of Dirichlet problem for biharmonic equation in the ball”, Complex Variables and Elliptic Equations, 64:9 (2019), 1500–1521 https://www.tandfonline.com/eprint/U28xHRrDURAMce7APwn9/full?target=10.1080/17476933.2018.1536702  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 3)
15. V. V. Karachik, B. Kh. Turmetov, “On Greens function of the Robin problem for the Poisson equation”, Advances in Pure and Applied Mathematics, 10:3 (2019), 203–214  crossref  mathscinet  zmath  isi (cited: 3)  scopus (cited: 4)
16. V. V. Karachik, “The Green Function of the Dirichlet Problem for the Biharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 59:1 (2019), 66–81  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib  scopus (cited: 3)
17. V. V. Karachik, A. M. Sarsenbi, B. Kh. Turmetov, “On the solvability of the main boundary value problems for a nonlocal Poisson equation”, Turkish Journal of Mathematics, 43 (2019), 1604–1625  crossref  mathscinet  zmath  isi (cited: 2)  scopus (cited: 3)
18. V. V. Karachik, B. Kh. Turmetov, “On solvability of some nonlocal boundary value problems for polyharmonic equation”, Kazakh Mathematical Journal, 19:1 (2019), 39–49 http://www.math.kz/media/journal/journal2019-07-2683070.pdf  elib
19. Zalyapin V.I., Karpeta T.V., Karachik V.V., Kharitonova E.V., “Valerii Leizerovich Dilman. K 70-letiyu so dnya rozhdeniya”, Vestnik Yuzhno-Uralskogo gosudarstvennogo universiteta. Seriya: Matematika. Mekhanika. Fizika., 11:4 (2019), 80–86  mathnet  elib
20. V. V. Karachik, B. Kh. Turmetov, “On a class of Neumann type problems for polyharmonic equation”, AIP Conference Proceedings, 2172:030002 (2019), 1–6 https://aip.scitation.org/doi/abs/10.1063/1.5133491  crossref  isi  scopus

   2018
21. V. V. Karachik, “Solving a Problem of Robin Type for Biharmonic Equation”, Russian Mathematics, 62:2 (2018), 34–48 https://rdcu.be/bqQ8z  mathnet  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib  scopus (cited: 2)
22. V. V. Karachik, “Riquier-Neumann Problem for the Polyharmonic Equation in a Ball”, Differential Equations, 54:5 (2018), 648–657  crossref  crossref  mathscinet  zmath  zmath  isi (cited: 7)  elib  scopus (cited: 8)
23. V. V. Karachik, B. Kh. Turmetov, “On solvability of some boundary value problems for a biharmonic equation with periodic conditions”, Filomat, 32:3 (2018), 947–953  crossref  mathscinet  isi (cited: 6)  scopus (cited: 9)

   2019
24. V. V. Karachik, B. Kh. Turmetov, “On the Greens Function for the Third Boundary Value Problem”, Siberian Advances in Mathematics, 29:1 (2019), 3243  mathnet  mathnet  crossref  crossref  mathscinet  elib  scopus (cited: 2)

   2018
25. V. V. Karachik, “Ob odnom predstavlenii funktsii Grina zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Vestnik YuUrGU, Seriya Matematika. Mekhanika. Fizika, 10:4 (2018), 13–22 https://vestnik.susu.ru/mmph/issue/view/517  mathnet  crossref  mathscinet  elib
26. V. V. Karachik, B. Kh. Turmetov, “O razreshimosti nekotorykh nelokalnykh kraevykh zadach dlya bigarmonicheskogo uravneniya”, Byulleten Instituta matematiki, 2018, no. 4, 16–22 http://mib.mathinst.uz/en/2018.html
27. V. V. Karachik, D. A. Komissarova, Matematicheskii analiz, Uchebnoe posobie, Chast II, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2018 , 158 pp.  zmath  elib

   2017
28. V. V. Karachik, B. T. Torebek, “On the DirichletRiquier Problem for Biharmonic Equations”, Mathematical Notes, 102:1 (2017), 31–42  mathnet  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib  elib  scopus (cited: 7)
29. V. V. Karachik, “O zadache tipa Robena dlya bigarmonicheskogo uravneniya v edinichnom share”, Problemy vychislitelnoi i prikladnoi matematiki, 2017, no. 1(7), 4-10  elib
30. V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Advances in Mathematics, 27:2 (2017), 103118  mathnet (cited: 8)  crossref  mathscinet  scopus (cited: 12)
31. V. V. Karachik, “Integral identities on a sphere for normal derivatives of polyharmonic functions”, SIBERIAN ELECTRONIC MATHEMATICAL REPORTS, 14 (2017), 533–551  mathnet  crossref  mathscinet  zmath  zmath  isi  elib  scopus
32. V. V. Karachik, “Generalized Third Boundary Value Problem for the Biharmonic Equation”, Differential Equations, 53:6 (2017), 756–765  crossref  crossref  mathscinet  zmath  zmath  isi (cited: 3)  elib  elib  scopus (cited: 5)
33. V. V. Karachik, B. Kh. Turmetov, “Solvability of some Neumann-type boundary value problems for biharmonic equations”, Electronic Journal of Differential Equations, 2017:218 (2017), 1–17 https://ejde.math.txstate.edu/Volumes/2017/218/karachik.pdf  mathscinet  zmath  isi  scopus (cited: 7)
34. V. V. Karachik, “Neumann type problem for polyharmonic equation in a ball”, Chelyab. Fiz.-Mat. Zh., 2:4 (2017), 420–429  mathnet  mathscinet  elib

   2016
35. H. Yuan, V. V. Karachik, “Representations of super-holomorphic functions and their applications”, Complex Variables and Elliptic Equations, 61:11 (2016), 1517–1532  crossref  mathscinet  zmath  isi (cited: 1)  scopus
36. V. V. Karachik, B. T. Torebek, “On an Uniqueness and Correct Solvability of the Biharmonic Boundary Value Problem”, ICAAM 2016 (Almaty, Kazakhstan September 7-10, 2016), AIP Conference Proceedings, 1759, 2016, 020045-1 020045-4  crossref  isi (cited: 1)  scopus (cited: 1)
37. V. V. Karachik, S. K. Masanov, B. Kh. Turmetov, “On solvability of some boundary value problems for a biharmonic equation with periodic conditions”, AIP Conference Proceedings, 1759:020118 (2016), 020118-1-020118-6 http://dx.doi.org/10.1063/1.4959732  crossref  isi  scopus
38. V. V. Karachik, B. T. Torebek, “On one mathematical model described by boundary value problem for the biharmonic equation”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 40–52  mathnet (cited: 3)  crossref  zmath  isi (cited: 3)  elib  scopus (cited: 3)
39. B. Kh. Turmetov, V. V. Karachik, “About one boundary value problem for the biharmonic equation”, AIP Conference Proceedings, 1789:040015 (2016), 040015-1040015-6 http://aip.scitation.org/toc/apc/1789/1?expanded=1789  crossref  isi (cited: 1)  scopus (cited: 1)

   2017
40. V. V. Karachik, “A Neumann-type problem for the biharmonic equation”, Siberian Adv. Math., 27:2 (2017), 103–118  mathnet  crossref  crossref  mathscinet  zmath  elib  elib  scopus (cited: 12)

   2016
41. V. L. Dil'man, V. I. Zalyapin, V. V. Karachik, L. D. Menikhes, “Mikhail Markovich Kipnis. To the seventy-five years anniversary”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 8:4 (2016), 70–75  mathnet

   2015
42. V. V. Karachik, “Cauchy and Goursat problems for differential equation of third order”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 7:2 (2015), 31–43  mathnet  elib
43. V. V. Karachik, “Solution of the Dirichlet Problem with Polynomial Data for the Polyharmonic Equation in a Ball”, Differential Equations, 51:8 (2015), 10331042  crossref  crossref  mathscinet  zmath  isi (cited: 14)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 15)
44. L. D. Menikhes, V. V. Karachik, “On the regularizability conditions of integral equations”, Ob usloviyakh regulyarizuemosti integralnykh uravnenii, Vestnik YuUrGU. Seriya Matematicheskoe modelirovanie i programmirovanie, 8:3 (2015), 142–148 http://mmp.vestnik.susu.ac.ru/pdf/v8n3st9.pdf  mathnet  crossref  isi  elib (cited: 1)  scopus
45. V. V. Karachik, M. A. Sadybekov, B. T. Torebek, “Uniqueness of solutions to boundary-value problems for the biharmonic equation in a ball”, Electronic Journal of Differential Equations, 2015 (2015), 1–9  mathscinet  isi (cited: 18)  scopus (cited: 18)
46. V. V. Karachik, Hong Fen, Yuan, “Dunkl-Poisson Equation and Related Equations in Superspace”, Mathematical Modelling and Analysis, 20:6 (2015), 768-781 http://www.tandfonline.com/doi/abs/10.3846/13926292.2015.1112856  crossref  mathscinet  isi (cited: 2)  scopus (cited: 2)
47. V. I. Zalyapin, V. V. Karachik, L. D. Menikhes, Ye. V. Kharitonova, “Boris Anisimovitch Bondarenko. To the 90-th anniversary”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 7:1 (2015), 65–67  mathnet  elib
48. V. V. Karachik, L. D. Menikhes, Teoriya funktsii kompleksnogo peremennogo, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2015 , 411 pp.  zmath  elib

   2014
49. V. V. Karachik, B. Kh. Turmetov, A. Bekaeva, “Solvability of some boundary-value problems for polyharmonic equation with Hadamard-Marchaud boundary operator”, Russian Mathematics, 58:7 (2014), 11–24  mathnet  mathnet  crossref  mathscinet  zmath  elib (cited: 1)  elib (cited: 1)  scopus (cited: 5)
50. V. V. Karachik, “Construction of Polynomial Solutions to the Dirichlet Problem for the Polyharmonic Equation in a Ball”, Computational Mathematics and Mathematical Physics, 54:7 (2014), 11221143  mathnet  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 18)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 19)
51. V. V. Karachik, “On the Arithmetic Triangle Arising from the Solvability Conditions for the Neumann Problem”, Math. Notes, 96:2 (2014), 217–227  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 8)
52. V. V. Karachik, Metod normirovannykh sistem funktsii, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 452 pp.  zmath  elib
53. V. V. Karachik, “Postroenie resheniya zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share s polinomialnymi dannymi”, Sistemy kompyuternoi matematiki i ikh prilozheniya, Materialy XV mezhdunarodnoi nauchnoi konferentsii (Smolensk, 16-18 maya 2014 g.), Izdatelstvo SmolGU, 2014, 153–155  elib
54. V. V. Karachik, “On a nonclassical boundary value problem for the Helmholtz equation”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 6:3 (2014), 14–22  mathnet
55. V. V. Karachik, “Solvability Conditions for the Neumann Problem for the Homogeneous Polyharmonic Equation”, Differential Equations, 50:11 (2014), 1449–1456  crossref  crossref  mathscinet  zmath  isi (cited: 18)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 21)
56. V. V. Karachik, “Reshenie zadachi Dirikhle dlya poligarmonicheskogo uravneniya v share”, Vestnik Natsionalnogo issledovatelskogo yadernogo universiteta MIFI, 3:6 (2014), 649–655  crossref  elib (cited: 1)
57. V. V. Karachik, “Green Function of the Dirichlet Boundary Value Problem for Polyharmonic Equation in a Ball Under Polynomial Data”, Izv. Saratov. Univ. Mat. Mekh. Inform., 14:4(2) (2014), 550–558  mathnet  crossref  elib
58. V. I. Zalyapin, V. V. Karachik, L. R. Kim-Tyan, L. D. Menikhes, Yu. B. Rusak, “Boris Vladimirovich Loginov. K 75-letiyu so dnya rozhdeniya”, Vestnik YuUrGU. Seriya Matematika. Mekhanika. Fizika, 6:4 (2014), 59–62  mathnet  zmath
59. V. V. Karachik, D. A. Komissarova, Matematicheskii analiz, uchebnoe posobie dlya samostoyatelnoi raboty, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 87 pp.
60. V. V. Karachik, Ryady Fure, 2-e izd., Izdatelskii tsentr YuUrGU, Chelyabinsk, 2014 , 126 pp.  zmath  elib

   2013
61. V. V. Karachik, “On some special polynomials and functions”, Sib. Èlektron. Mat. Izv., 10 (2013), 205–226  mathnet  elib  scopus
62. V. V. Karachik, “Rows of Pascal's triangle modulo a prime”, Diskretn. Anal. Issled. Oper., 20:2 (2013), 26–46  mathnet  mathscinet  elib
63. V. V. Karachik, “On the mean-value property for polyharmonic functions”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 6:3 (2013), 59–66  mathnet

   2014
64. V. V. Karachik, “On solvability conditions for the Neumann problem for a polyharmonic equation in the unit ball”, Journal of Applied and Industrial Mathematics, 8:1 (2014), 63–75  mathnet  crossref  mathscinet  elib  scopus (cited: 20)
65. V. V. Karachik, “On the mean value property for polyharmonic functions in the ball”, Siberian Advances in Mathematics, 24:3 (2014), 169–182  mathnet  crossref  mathscinet  elib  scopus (cited: 8)

   2013
66. V. V. Karachik, N. A. Antropova, “Polynomial solutions of the Dirichlet problem for the biharmonic equation in the ball”, Differential Equations, 49:2 (2013), 251–256  crossref  mathscinet  mathscinet  zmath  isi (cited: 18)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 17)
67. V. V. Karachik, “On an arithmetical triangle”, Journal of Mathematical Sciences, 195:5 (2013), 665–675  crossref  mathscinet  zmath  scopus (cited: 1)
68. V. V. Karachik, “On one generalized mean theorem for harmonic functions”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 5:1 (2013), 34–39  mathnet
69. R. Zh. Aleev, V. L. Dil'man, A. D. Drozin, V. I. Zalyapin, V. V. Karachik, A. V. Keller, Yu. M. Kovalev, N. A. Manakova, G. A. Sviridyuk, E. V. Tabarintseva, “Leonid Menikhes (to the $65^{th}$ anniversary)”, Vestnik YuUrGU, 6:3 (2013), 136–140  mathnet

   2012
70. V. V. Karachik, “Application of the Almansi formula for constructing polynomial solutions to the Dirichlet problem for a second-order equation”, Russian Math. (Iz. VUZ), 56:6 (2012), 20–29  mathnet  crossref  mathscinet  scopus (cited: 2)
71. V. V. Karachik, “Method for constructing solutions of linear ordinary differential equations with constant coefficients”, Comput. Math. Math. Phys., 52:2 (2012), 219–234  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 5)
72. Karachik V.V., Antropova N.A., “O polinomialnykh resheniyakh zadachi Dirikhle dlya bigarmonicheskogo uravneniya v share”, Sibirskii zhurnal industrialnoi matematiki, XV:2, (50) (2012), 86-98  mathnet (cited: 11)  mathscinet  zmath  elib (cited: 16)
73. Valery V. Karachik, “Polynomial solutions to Dirihlet boundary value problem for the $3$-harmonic equation in a ball”, J. Sib. Fed. Univ. Math. Phys., 5:4 (2012), 527–546  mathnet  elib
74. V. V. Karachik, B. Kh. Turmetov, A. Bekaeva, “Solvability conditions of the Neumann boundary value problem for the biharmonic equation in the unit ball”, International Journal of Pure and Applied Mathematics, 81:3 (2012), 487–495  zmath  scopus (cited: 24)
75. V. V. Karachik, “Pascals triangle and $p$-latin matrices”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2012, no. 7, 17–30  mathnet
76. V. V. Karachik, B. K. Turmetov, B. T. Torebek, “On some integro-differential operators in the class of harmonic functions and their applications”, Siberian Adv. Math., 22:2 (2012), 115–134  mathnet  crossref  mathscinet  elib (cited: 13)  elib (cited: 13)  scopus (cited: 16)

   2011
77. V. V. Karachik, “Construction of polynomial solutions to some boundary value problems for Poisson's equation”, Computational Mathematics and Mathematical Physics, 51:9 (2011), 1567-1587  mathnet  crossref  mathscinet  zmath  isi (cited: 26)  elib  scopus (cited: 27)
78. V. V. Karachik, N. A. Antropova, “Construction of polynomial solutions to the Dirichlet problem for the biharmonic equation in a ball”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 5, 39–50  mathnet  elib
79. V. V. Karachik, “Polynomial solutions to partial differential equations with constant coefficients II”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 5, 27–38  mathnet
80. V. V. Karachik, “Polinomialnye resheniya differentsialnykh uravnenii v chastnykh proizvodnykh s postoyannymi koeffitsientami I”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 2011, no. 4, 4–17  mathnet (cited: 7)

   2010
81. V. V. Karachik, N. A. Antropova, “On the solution of a nonhomogeneous polyharmonic equation and the nonhomogeneous Helmholtz equation”, Differential Equations, 46:3 (2010), 387-399  crossref  mathscinet  zmath  isi (cited: 8)  elib (cited: 9)  elib (cited: 9)  scopus (cited: 12)
82. V. V. Karachik, “Almansi decompositions for non-singular second order partial differential operators”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2010, no. 3, 4–12  mathnet

   2009
83. V. V. Karachik, Kurs matematicheskogo analiza, Izdatelskii tsentr YuUrGU, Chelyabinsk, 2009 , 682 pp.  zmath  elib

   2008
84. V. V. Karachik, “On an Expansion of Almansi Type”, Math. Notes, 83:3 (2008), 335–344  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 6)
85. V. V. Karachik, Matematicheskii analiz, uchebnoe posobie dlya studentov inzhenerno-fizicheskikh i fiziko-matematicheskikh spetsialnostei universitetov, v. 2, Yuzhno-Uralskii gosudarstvennyi universitet, Chelyabinsk, 2008 , 267 pp.  zmath  elib
86. V. V. Karachik, Matematicheskii analiz, uchebnoe posobie dlya studentov inzhenerno-fizicheskikh i fiziko-matematicheskikh spetsialnostei universitetov, v. 1, Yuzhno-Uralskii gosudarstvennyi universitet, Chelyabinsk, 2008 , 154 pp.  zmath  elib
87. V. V. Karachik, “On One Representation of Analytic Functions by Harmonic Functions”, Siberian Adv. Math., 18:2 (2008), 103–117  mathnet  crossref  mathscinet  elib (cited: 3)  elib (cited: 3)  scopus (cited: 1)

   2004
88. V. V. Karachik, “On some special polynomials”, Proceedings of American Mathematical Society, 132:4 (2004), 1049-1058  crossref  mathscinet  zmath  isi (cited: 10)

   2003
89. V. V. Karachik, “Normalized system of functions with respect to the Laplace operator and its applications”, J. Math. Anal. Appl., 287:2 (2003), 577–592  crossref  mathscinet  zmath  isi (cited: 31)  scopus (cited: 35)
90. V. V. Karachik, “Polynomial Solutions to the Lamé Equations”, Siberian Adv. Math., 13:2 (2003), 66–79  mathnet  mathscinet  zmath

   2000
91. V. V. Karachik, “Polynomial solutions to the systems of partial differential equations with constant coefficients”, Yokohama Math. J., 2000, no. 47, 121–142  mathscinet  zmath

   1999
92. V. V. Karachik, “A generalized Neumann problem for harmonic functions in the half-space”, Differential Equations, 35:7 (1999), 949–955  mathnet  mathscinet  zmath  isi (cited: 2)

   1998
93. V. V. Karachik, “On one set of orthogonal harmonic polynomials”, Proceedings of American Mathematical Society, 126:12 (1998), 3513-3519  crossref  mathscinet  zmath  isi (cited: 19)

   1997
94. V. V. Karachik, “Harmonic polynomials and the divisibility problem”, PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 125:11 (1997), 3257–3258  crossref  mathscinet  zmath  isi
95. V. V. Karachik, “Continuity of polynomial solutions with respect to the coefficient of the higher derivative”, INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 28:9 (1997), 1229–1234  mathscinet  zmath  isi (cited: 2)

   1996
96. V. V. Karachik, “A problem with higher-order normal derivatives on the boundary for the Poisson equation”, Differential Equations, 32:3 (1996), 421–424  mathnet  mathscinet  zmath  isi (cited: 4)
97. V. V. Karachik, “P-Latin matrices and Pascal's triangle modulo a prime”, The Fibonacci Quarterly, 1996, no. 34(4), 362–372  mathscinet  zmath  isi (cited: 5)

   1992
98. V. V. Karachik, “O pazpeshimosti kpaevoi zadachi dlya upavneniya Gelmgoltsa s nopmalnymi ppoizvodnymi vysokogo popyadka na gpanitse”, Differentsialnye uravneniya, 28:5 (1992), 907–909  mathnet (cited: 1)  mathscinet  zmath

   1991
99. V. V. Karachik, “Postpoenie polinomialnykh peshenii diffepentsialnykh upavnenii s postoyannymi koeffitsientami”, Differentsialnye uravneniya, 27:3 (1991), 534–535  mathnet (cited: 2)  mathscinet  zmath
100. V. V. Karachik, “A problem for the polyharmonic equation in the sphere”, Siberian Mathematical Journal, 32:5 (1991), 767–774  mathnet  crossref  mathscinet  zmath  isi (cited: 16)  scopus (cited: 20)
101. V. V. Karachik, “O pazpeshimosti odnoi zadachi s nopmalnymi ppoizvodnymi vysokogo popyadka na gpanitse”, DAN UzSSR, 1991, no. 6, 8–11  mathscinet  elib

   1990
102. V. V. Karachik, B. Kh. Turmetov, “Ob odnoi zadache dlya gapmonicheskogo upavneniya”, Izvestiya AN UzSSR, sep. fiz.-mat. nauk, 1990, no. 4, 17–21  mathscinet  zmath  elib
103. V. V. Karachik, G. Saidkapimova, “O pazpeshimosti zadachi Gupsa dlya lineinogo upavneniya Manzhepona s postoyannymi koeffitsientami”, DAN UzSSR, 1990, no. 9, 7–9  mathscinet  zmath  elib

   1989
104. V. V. Karachik, “Nekotopyi klass zadach dlya poligapmonicheskogo upavneniya v shape”, DAN UzSSR, 1989, no. 9, 7–8  mathscinet  zmath  elib

   1987
105. V. V. Karachik, B. A. Bondarenko, “Analogi formuly Eilera dlya obobschennoodnopodnykh funktsii”, DAN UzSSR, 1987, no. 5, 5–7  mathscinet  zmath  elib

   1977
106. V. V. Karachik, “Dinamika sistem n pap “khischnik-zheptva” svyazannykh po konkupentsii”, Izvestiya AN UzSSR, sepiya tekhn. nauk, 1977, no. 6, 3–9

Presentations in Math-Net.Ru
1. On polynomial solutions of the Dirichlet problem for the polyharmonic equation in a ball
V. V. Karachik
International Conference on Differential Equations and Dynamical Systems
July 7, 2014 15:00

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