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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 2, Pages 133–166 (Mi izv429)  

This article is cited in 21 scientific papers (total in 21 papers)

Uniqueness theorems for linear non-local problems for abstract differential equations

I. V. Tikhonov


Abstract: The paper deals with linear non-local problems for differential equations in Banach spaces. We prove a criterion for uniqueness of solution and obtain some corollaries and generalizations.

DOI: https://doi.org/10.4213/im429

Full text: PDF file (3162 kB)
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English version:
Izvestiya: Mathematics, 2003, 67:2, 333–363

Bibliographic databases:

UDC: 517.954
MSC: 34G99, 47R50, 35Q30
Received: 21.11.2001

Citation: I. V. Tikhonov, “Uniqueness theorems for linear non-local problems for abstract differential equations”, Izv. RAN. Ser. Mat., 67:2 (2003), 133–166; Izv. Math., 67:2 (2003), 333–363

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Popov A. Yu., Tikhonov I. V., “Uniqueness classes in a time-nonlocal problem for the heat equation and complex eigenfunctions of the Laplace operator”, Differ. Equ., 40:3 (2004), 428–437  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    2. Tikhonov I.V., Èidelman Yu.S., “Spectral mapping theorems for point spectra for $C_0$-semigroups and their applications to uniqueness problems for abstract differential equations”, Dokl. Math., 69:1 (2004), 26–29  mathnet  mathscinet  zmath  isi  elib
    3. Kraposhin V.S., D'yakonova N.B., Lyasotskii I.V., Yan'tszin W., “Cluster model of formation of an incommensurate $\omega$-phase in alloys of the titanium–iron system”, Metal Science and Heat Treatment, 46:5-6 (2004), 250–255  crossref  isi  elib  scopus
    4. Prilepko A. I., “The semigroup method for inverse, nonlocal, and nonclassical problems. Prediction-control and prediction-observation for evolution equations. I”, Differ. Equ., 41:11 (2005), 1635–1646  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    5. A. Yu. Popov, I. V. Tikhonov, “Exponential solubility classes in a problem for the heat equation with a non-local condition for the time averages”, Sb. Math., 196:9 (2005), 1319–1348  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. P. Zastavnyi, “On Zeros of Entire Functions of Special Form”, Math. Notes, 83:1 (2008), 23–30  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. V. E. Fedorov, N. D. Ivanova, Yu. Yu. Fedorova, “On a time nonlocal problem for inhomogeneous evolution equations”, Siberian Math. J., 55:4 (2014), 721–733  mathnet  crossref  mathscinet  isi
    8. A. V. Glushak, “Abstract Euler–Poisson–Darboux equation with nonlocal condition”, Russian Math. (Iz. VUZ), 60:6 (2016), 21–28  mathnet  crossref  isi
    9. A. I. Kozhanov, G. A. Lukina, “Nelokalnye zadachi s integralnym usloviem dlya differentsialnykh uravnenii nechetnogo poryadka”, Sib. elektron. matem. izv., 13 (2016), 452–466  mathnet  crossref  mathscinet
    10. I. V. Tikhonov, Yu. V. Gavris, T. Z. Adzhieva, “Struktura reshenii modelnoi obratnoi zadachi teploprovodnosti v klassakh funktsii eksponentsialnogo rosta”, Chelyab. fiz.-matem. zhurn., 1:3 (2016), 37–62  mathnet
    11. T. K. Yuldashev, “Obratnaya zadacha dlya obyknovennogo integro-differentsialnogo uravneniya s vyrozhdennym yadrom i nelokalnymi integralnymi usloviyami”, Vestnik TvGU. Seriya: Prikladnaya matematika, 2016, no. 3, 19–33  mathnet  crossref  elib
    12. T. K. Yuldashev, “Obyknovennoe integro-differentsialnoe uravnenie s vyrozhdennym yadrom i integralnym usloviem”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 20:4 (2016), 644–655  mathnet  crossref  zmath  elib
    13. I. V. Tikhonov, V. N. Shon Tung, “Formuly yavnogo resheniya v modelnoi nelokalnoi zadache dlya uravneniya prostogo perenosa”, Matematicheskie zametki SVFU, 24:1 (2017), 57–73  mathnet  elib
    14. A. V. Glushak, “Uniquely solvable problems for abstract Legendre equation”, Russian Math. (Iz. VUZ), 62:7 (2018), 1–12  mathnet  crossref  isi
    15. Boito P., Eidelman Y., Gemignani L., “Efficient Solution of Parameter-Dependent Quasiseparable Systems and Computation of Meromorphic Matrix Functions”, Numer. Linear Algebr. Appl., 25:6, SI (2018), e2141  crossref  mathscinet  zmath  isi  scopus
    16. T. K. Yuldashev, “Ob odnoi kraevoi zadache dlya integro-differentsialnogo uravneniya v chastnykh proizvodnykh chetvertogo poryadka s vyrozhdennym yadrom”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 145, VINITI RAN, M., 2018, 95–109  mathnet  mathscinet
    17. S. N. Melikhov, “Koeffitsienty ryadov eksponent dlya analiticheskikh funktsii i operator Pomme”, Kompleksnyi analiz. Tselye funktsii i ikh primeneniya, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 161, VINITI RAN, M., 2019, 65–103  mathnet  mathscinet
    18. Kozhanov A.I., “Nonlocal Problems With Integral Conditions For Elliptic Equations”, Complex Var. Elliptic Equ., 64:5 (2019), 741–752  crossref  mathscinet  zmath  isi  scopus
    19. T. K. Yuldashev, “Spektralnye osobennosti resheniya odnoi kraevoi zadachi dlya integro-differentsialnogo uravneniya Fredgolma vtorogo poryadka s otrazheniem argumenta”, Izv. IMI UdGU, 54 (2019), 122–134  mathnet  crossref
    20. A. V. Glushak, “Nelokalnaya zadacha dlya abstraktnogo uravneniya Besselya–Struve”, Izv. vuzov. Matem., 2019, no. 7, 29–38  mathnet  crossref
    21. T. K. Yuldashev, “Ob osobennostyakh resheniya odnoi kraevoi zadachi dlya mnogomernogo integro-differentsialnogo uravneniya Benni—Lyuka so spektralnymi parametrami”, Geometriya i mekhanika, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 174, VINITI RAN, M., 2020, 109–129  mathnet  crossref
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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