Qualitative theory of partial differential equations, singular solutions and the behavior of solutions of nonlinear ordinary differential equations.
Main publications:
Konkov A. A. O svoistvakh reshenii ellipticheskikh neravenstv s nelineinostyu v glavnoi chasti // Doklady RAN. 2002. T. 383. No. 1. S. 15–19.
Konkov A. A. Teoremy sravneniya dlya ellipticheskikh neravenstv s nelineinostyu v glavnoi chasti (soobschenie MMO) // UMN. 2002. T. 57. Vyp. 3. S. 141–142.
Konkov A. A. Povedenie reshenii ellipticheskikh neravenstv v oblastyakh proizvolnoi geometrii // Doklady RAN. 2002. T. 387. No. 5.
Konkov A. A. O nekotorykh apriornykh otsenkakh dlya reshenii sistem obyknovennykh differentsialnykh uravnenii tipa Emdena–Faulera // Matem. zametki. 2003. T. 73. Vyp. 5. S. 792–796.
Kon'kov A. A. Behavior of solutions of quasilinear parabolic inequalities // Russ. J. Math. Phys. 2003. T. 10. No. 4. S. 467–472.
Konkov A. A. Povedenie reshenii kvazilineinykh ellipticheskikh neravenstv // Sovremennaya matematika. Fundamentalnye napravleniya. T. 7. Moskva, 2004.
Konkov A. A. Teoremy sravneniya dlya divergentnykh ellipticheskikh neravenstv, soderzhaschikh chleny s mladshimi proizvodnymi // UMN. 2004. T. 59. Vyp. 5. S. 151–152.
Kon'kov A. A. On non-extendable solutions of ordinary differential equation // J. Math. Analysis and Appl. 2004. T. 298. No. 1. S. 184–209.
Kon'kov A. A. Comparison theorems for second-order elliptic inequalities // Nonlinear Analysis. Theory, Methods and Appl. 2004. T. 59. No. 4. S. 583–608.
Kon'kov A. A. Stabilization of solutions of nonlinear parabolic inequalities // Russ. J. Math. Phys. 2005. T. 12. No. 2. S. 197–204.
Kon'kov A. A. On the asymptotic behaviour of solutions of nonlinear parabolic equations // Proc. Royal Soc. of Edinburgh. 2006. T. 136. S. 365–384.
Konkov A. A. Povedenie reshenii ellipticheskikh neravenstv, nelineinykh otnositelno starshikh proizvodnykh // Izvestiya RAN. Ser. matem. 2007. T. 71. No. 1. S. 17–37.
Kon'kov A. A. Comparison theorems for elliptic inequalities with a non-linearity in the principal part // J. Math. Analysis and Appl. 2007. T. 325. S. 1013–1041.
Konkov A. A. O svoistvakh reshenii odnogo klassa nelineinykh obyknovennykh differentsialnykh uravnenii // Trudy Seminara im. I.G.Petrovskogo. 2007. T. 26. S. 194-221.
Konkov A. A. Ob odnom uslovii otsutstviya globalnykh reshenii u neavtonomnykh obyknovennykh differentsialnykh uravnenii // Diff. ur-ya. 2007. T. 43. No. 11. S. 1574.
Konkov A. A. Ob otsutstvii globalnykh reshenii u radialnogo uravneniya p-Laplasa // UMN. 2008. T. 63. Vyp. 1. S. 161-162.
Konkov A. A. O resheniyakh obyknovennykh differentsialnykh uravnenii, imeyuschikh vertikalnuyu asimptotu // Matem. sb. 2008. T. 199. No. 1. S. 3-14.
Kon'kov A. A. On global solutions of the radial p-Laplace equation // Nonlinear Analysis. Theory, Methods and Appl. 2009. T. 70. S. 3437-3451.
S. M. Bakiev, A. A. Kon'kov, “On the Existence of Solutions of the Dirichlet Problem for the $p$-Laplacian on Riemannian Manifolds”, Mat. Zametki, 114:5 (2023), 659–668; Math. Notes, 114:5 (2023), 679–686
2022
2.
A. A. Kon'kov, “On the absence of global solutions of a system of ordinary differential equations”, Mat. Sb., 213:3 (2022), 41–63; Sb. Math., 213:3 (2022), 319–340
A. A. Kon'kov, “Comparison theorems for elliptic inequalities with lower-order derivatives that take into account the geometry of the domain”, Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021), 35–39; Dokl. Math., 104:2 (2021), 250–253
4.
V. V. Brovkin, A. A. Kon'kov, “Existence of Solutions to the Second Boundary-Value Problem for the $p$-Laplacian on Riemannian Manifolds”, Mat. Zametki, 109:2 (2021), 180–195; Math. Notes, 109:2 (2021), 171–183
A. A. Kon'kov, “On the stabilization of solutions of nonlinear parabolic equations with lower-order derivatives”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 220–238; J. Math. Sci. (N. Y.), 244:2 (2020), 254–266
A. A. Kon'kov, A. E. Shishkov, “On the Absence of Global Solutions of a Class of Higher-Order Evolution Inequalities”, Mat. Zametki, 104:6 (2018), 945–947; Math. Notes, 104:6 (2018), 930–932
2017
8.
A. A. Kon'kov, “Blow-up of solutions for a class of nondivergence elliptic inequalities”, Zh. Vychisl. Mat. Mat. Fiz., 57:3 (2017), 448–458; Comput. Math. Math. Phys., 57:3 (2017), 453–463
A. A. Kon'kov, “On Estimates of Solutions to Elliptic Inequalities near a Singular Point”, Mat. Zametki, 99:4 (2016), 623–625; Math. Notes, 99:4 (2016), 608–610
10.
A. A. Kon'kov, “Maximum principle for nonlinear parabolic equations”, Tr. Semim. im. I. G. Petrovskogo, 31 (2016), 63–86; J. Math. Sci. (N. Y.), 234:4 (2018), 423–439
A. A. Kon'kov, “On the maximum principle for a class of nonlinear parabolic equations”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2015, no. 6(128), 89–92
2014
12.
A. A. Kon'kov, “On comparison theorems for quasi-linear elliptic inequalities with a special account of the geometry of the domain”, Izv. RAN. Ser. Mat., 78:4 (2014), 123–174; Izv. Math., 78:4 (2014), 758–808
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, N. A. Izobov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. V. Palin, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, E. V. Radkevich, O. S. Rozanova, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Scientific heritage of Vladimir Mikhailovich Millionshchikov”, Tr. Semim. im. I. G. Petrovskogo, 30 (2014), 5–41; J. Math. Sci. (N. Y.), 210:2 (2015), 115–134
2013
14.
A. A. Kon'kov, “Stabilization of solutions of the nonlinear Fokker–Planck equation”, Tr. Semim. im. I. G. Petrovskogo, 29 (2013), 333–345; J. Math. Sci. (N. Y.), 197:3 (2014), 358–366
A. A. Kon'kov, “On the absence of global solutions of the radial $p$-Laplace equation”, Uspekhi Mat. Nauk, 63:1(379) (2008), 161–162; Russian Math. Surveys, 63:1 (2008), 161–162
17.
A. A. Kon'kov, “Solutions of ordinary differential equations with vertical asymptote”, Mat. Sb., 199:1 (2008), 3–14; Sb. Math., 199:1 (2008), 1–11
2007
18.
A. A. Kon'kov, “The behaviour of solutions of elliptic inequalities that are non-linear with respect to the highest derivatives”, Izv. RAN. Ser. Mat., 71:1 (2007), 17–54; Izv. Math., 71:1 (2007), 15–51
A. A. Kon'kov, “On properties of solutions of a class of nonlinear ordinary differential equations”, Tr. Semim. im. I. G. Petrovskogo, 26 (2007), 195–222; J. Math. Sci. (N. Y.), 143:4 (2007), 3303–3321
A. A. Kon'kov, “Behavior of Solutions of Quasilinear Elliptic Inequalities”, CMFD, 7 (2004), 3–158; Journal of Mathematical Sciences, 134:3 (2006), 2073–2237
A. A. Kon'kov, “Comparison theorems for elliptic divergence inequalities containing
terms with lower derivatives”, Uspekhi Mat. Nauk, 59:5(359) (2004), 151–152; Russian Math. Surveys, 59:5 (2004), 961–962
2003
22.
A. A. Kon'kov, “A Priori Estimates for Solutions of Ordinary Differential Equations of Emden–Fowler Type”, Mat. Zametki, 73:5 (2003), 792–796; Math. Notes, 73:5 (2003), 747–750
A. A. Kon'kov, “Comparison theorems for elliptic inequalities with a non-linearity in the principal part”, Uspekhi Mat. Nauk, 57:3(345) (2002), 141–142; Russian Math. Surveys, 57:3 (2002), 599–600
A. A. Kon'kov, “Nonnegative solutions of quasilinear elliptic inequalities in domains contained in a layer”, Differ. Uravn., 36:7 (2000), 889–897; Differ. Equ., 36:7 (2000), 988–997
A. A. Kon'kov, “On solutions of quasilinear elliptic inequalities vanishing in a neighborhood of infinity”, Mat. Zametki, 67:1 (2000), 153–156; Math. Notes, 67:1 (2000), 122–125
A. A. Kon'kov, “Behavior of solutions of quasilinear elliptic inequalities containing terms with lower-order derivatives”, Mat. Zametki, 64:6 (1998), 946–949; Math. Notes, 64:6 (1998), 817–821
A. A. Kon'kov, “Behavior at infinity of solutions of second-order nonlinear equations of a particular class”, Mat. Zametki, 60:1 (1996), 30–39; Math. Notes, 60:1 (1996), 22–28
A. A. Kon'kov, “On the solution space of elliptic equations on Riemannian manifolds”, Differ. Uravn., 31:5 (1995), 805–813; Differ. Equ., 31:5 (1995), 745–752
A. A. Kon'kov, “Maximum principle for elliptic equations on smooth Riemannian manifolds”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 4, 10–14
1994
34.
V. A. Kondrat'ev, A. A. Kon'kov, “On properties of solutions of a class of nonlinear second-order equations”, Mat. Sb., 185:9 (1994), 81–94; Russian Acad. Sci. Sb. Math., 83:1 (1995), 67–77
A. A. Kon'kov, “On the dimension of the solution space of elliptic systems in unbounded domains”, Mat. Sb., 184:12 (1993), 23–52; Russian Acad. Sci. Sb. Math., 80:2 (1995), 411–434
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Goritsky, N. V. Denisova, Yu. S. Ilyashenko, T. O. Kapustina, A. A. Kon'kov, V. V. Palin, E. V. Radkevich, V. V. Rogachev, O. S. Rozanova, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, M. V. Shamolin, T. A. Shaposhnikova, “К 70-летию Валерия Васильевича Козлова”, Tr. Semim. im. I. G. Petrovskogo, 33 (2023), 3–7
2019
37.
Yu. A. Alkhutov, V. F. Butuzov, V. V. Kozlov, A. A. Kon'kov, A. V. Mikhalev, E. I. Moiseev, E. V. Radkevich, N. Kh. Rozov, V. A. Sadovnichii, I. N. Sergeev, M. D. Surnachev, R. N. Tikhomirov, V. N. Chubarikov, T. A. Shaposhnikova, A. A. Shkalikov, “Vasilii Vasilievich Zhikov”, Tr. Semim. im. I. G. Petrovskogo, 32 (2019), 5–7; J. Math. Sci. (N. Y.), 244:2 (2020), 113–115
2011
38.
M. S. Agranovich, I. V. Astashova, L. A. Bagirov, V. V. Vlasov, V. V. Zhikov, Yu. S. Ilyashenko, V. V. Kozlov, A. A. Kon'kov, S. I. Pokhozhaev, E. V. Radkevich, N. Kh. Rozov, I. N. Sergeev, A. L. Skubachevskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev. July 2, 1935 – March 11, 2010”, CMFD, 39 (2011), 5–10; Journal of Mathematical Sciences, 190:1 (2013), 1–7
39.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. Yu. Goritskii, N. V. Denisova, V. V. Zhikov, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, M. S. Romanov, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Olga Arsenjevna Oleinik”, Tr. Semim. im. I. G. Petrovskogo, 28 (2011), 5–7; J. Math. Sci. (N. Y.), 179:3 (2011), 345–346
2010
40.
I. V. Astashova, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, V. V. Kozlov, V. A. Kondratiev, A. A. Kon'kov, N. Kh. Rozov, I. N. Sergeev, V. N. Chubarikov, A. T. Fomenko, A. S. Shamaev, “To memory of Vladimir Mikhailovich Millionshchikov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2010, no. 2, 71–72
2007
41.
I. V. Astashova, L. A. Bagirov, A. V. Borovskikh, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, G. V. Grishina, N. V. Denisova, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, I. V. Matrosov, V. M. Millionshchikov, V. A. Nikishkin, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, V. A. Sadovnichii, V. S. Samovol, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, A. F. Filippov, T. S. Khachlaev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, “Vladimir Alexandrovich Kondratiev on the 70th anniversary of his birth”, Tr. Semim. im. I. G. Petrovskogo, 26 (2007), 5–28; J. Math. Sci. (N. Y.), 143:4 (2007), 3183–3197
2005
42.
V. A. Il'in, V. V. Kozlov, V. A. Sadovnichii, I. V. Astashova, A. A. Kon'kov, V. M. Millionshchikov, E. V. Radkevich, N. Kh. Rozov, A. V. Filinovskii, A. S. Shamaev, “Vladimir Aleksandrovich Kondrat'ev (A Tribute in Honor of His 70th Birthday)”, Differ. Uravn., 41:7 (2005), 867–873; Differ. Equ., 41:7 (2005), 909–914
43.
I. V. Astashova, L. A. Bagirov, V. V. Bykov, A. N. Vetokhin, A. Yu. Goritskii, G. V. Grishina, Yu. S. Ilyashenko, T. O. Kapustina, V. V. Kozlov, A. A. Kon'kov, O. B. Lupanov, I. V. Matrosov, V. M. Millionshchikov, V. A. Nikishkin, E. V. Radkevich, O. S. Rozanova, È. R. Rozendorn, N. Kh. Rozov, V. A. Sadovnichii, V. S. Samovol, I. N. Sergeev, I. V. Filimonova, A. V. Filinovskii, A. F. Filippov, T. S. Khachlaev, G. A. Chechkin, A. S. Shamaev, T. A. Shaposhnikova, A. A. Shkalikov, “Vladimir Aleksandrovich Kondrat'ev”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2005, no. 5, 77–79