Geodesic
Solvability of nonlocal problems for systems of Sobolev-type differential equations with a multipoint condition
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2019), pp. 3-15.

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We consider the nonlocal problem for system of loaded differential equations Sobolev-type with multi-point condition. By the method of introducing additional unknown functions the considered problem is reduced to an equivalent problem consisting of a nonlocal multi-point problem for a system of loaded hyperbolic equations second order with functional parameters and integral relations. Algorithms for finding solution to the equivalent problem are proposed. Conditions of well-posedness of the nonlocal multi-point problem for the system of loaded hyperbolic equations second order are obtained. The conditions of an existence unique classical solution to the nonlocal problem for the system of differential equations Sobolev-type with multi-point condition are established.
Keywords: system of differential equations Sobolev-type, algorithm, unique solvability.
Mots-clés : multi-point condition 
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     author = {A. T. Assanova and A. E. Imanchiyev and Zh. M. Kadirbayeva},
     title = {Solvability of nonlocal problems for systems of {Sobolev-type} differential equations with a multipoint condition},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
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A. T. Assanova; A. E. Imanchiyev; Zh. M. Kadirbayeva. Solvability of nonlocal problems for systems of Sobolev-type differential equations with a multipoint condition. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2019), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2019_12_a0/

[1] Algazin S. D., Kiiko I. A., Flatter plastin i obolochek, Nauka, M., 2006

[2] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995

[3] Boichuk A. A., Samoilenko A. M., Generalized inverse operators and Fredholm boundary-value problems, VSP, Utrecht, 2004 | MR | Zbl

[4] Brunner H., Collocation methods for Volterra integral and related functional equations, Cambridge Univ. Press, London, 2004 | MR | Zbl

[5] Nakhushev A. M., Zadachi so smescheniem dlya uravnenii v chastnykh proizvodnykh, Nauka, M., 2006

[6] Guezane-Lakoud A., Belakroum D., “Time-discretization schema for an integrodifferential Sobolev type equation with integral conditions”, Appl. Math. Comp., 218:9 (2012), 4695–4702 | DOI | MR | Zbl

[7] Babenko K. I., Teoreticheskie osnovy i konstruirovanie chislennykh algoritmov zadach matematicheskoi fiziki, Nauka, M., 1979

[8] Ptashnik B. I., Nekorrektnye granichnye zadachi dlya differentsialnykh uravnenii s chastnymi proizvodnymi, Nauk. dumka, Kiev, 1984

[9] Kiguradze T., “Some boundary value problems for systems of linear partial differential equations of hyperbolic type”, Mem. Diff. Equat. Math. Phys., 1 (1994), 1–144 | MR | Zbl

[10] Zhegalov V. I., Utkina E. A., “Ob odnom psevdoparabolicheskom uravnenii tretego poryadka”, Izv. vuzov. Matem., 1999, no. 10, 73–76

[11] Kiguradze T., Lakshmikantham V., “On initial-boundary value problems in bounded and unbounded domains for a class of nonlinear hyperbolic equations of the third order”, J. Math. Anal. Appl., 324:8 (2006), 1242–1261 | DOI | MR | Zbl

[12] Kiguradze I., Kiguradze T., “On solvability of boundary value problems for higher order nonlinear hyperbolic equations”, Nonlinear Anal., 69:5 (2008), 1914–1933 | DOI | MR | Zbl

[13] Andreev A. A., Yakovleva Yu. O., “Zadacha Gursa dlya odnoi sistemy giperbolicheskikh differentsialnykh uravnenii tretego poryadka s dvumya nezavisimymi peremennymi”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-matem. nauki, 24:3 (2011), 35–41 | DOI

[14] De Angelis M., Fiore G., “Existence and uniqueness of solutions of a class of third order dissipative problems with various boundary conditions describing the Josephson effect”, J. Math. Anal. Appl., 404:2 (2013), 477–490 | DOI | MR | Zbl

[15] Assanova A. T., Imanchiev A. E., “Solvability of multipoint-integral boundary value problem for a third-order differential equation and parametrization method”, Functional Analysis in Interdisciplinary Applications, Springer Proceedings in Mathematics Statistics, 216, eds. T. Sh. Kalmenov et al., Springer International Publ., Cham, 2017, 113–122 | DOI | MR | Zbl

[16] Assanova A. T., Imanchiev A. E., “On the solvability of a nonlocal boundary value problem for a loaded hyperbolic equations with multi-point conditions”, Bull. Karaganda Univ., Math., 81:1 (2016), 15–25 | MR

[17] Dzhenaliev M. T., Ramazanov M. I., Nagruzhennye uravneniya kak vozmuscheniya differentsialnykh uravnenii, Gylym, Almaty, 2010

[18] Nakhushev A. M., Nagruzhennye uravneniya i ikh primeneniya, Nauka, M., 2012

[19] Asanova A. T., Imanchiev A. E., Kadirbaeva Zh. M., “O chislennom reshenii sistem obyknovennykh nagruzhennykh differentsialnykh uravnenii s mnogotochechnymi usloviyami”, Zhurn. vychisl. matem. i matem. fiz., 58:4 (2018), 520–529 | DOI

[20] Utkina E. A., “Ob odnoi granichnoi zadache dlya funktsionalno-differentsialnogo giperbolicheskogo uravneniya tretego poryadka”, Izv. vuzov. Matem., 2016, no. 8, 69–73

[21] Asanova A. T., Dzhumabaev D. S., “Well-posedness of nonlocal boundary value problems with integral condition for the system of hyperbolic equations”, J. Math. Anal. Appl., 402:1 (2013), 167–178 | DOI | MR | Zbl