|1Yuldashev, TK |
1Siberian State Aerospace University, Krasnoyarsk, Russia
|Dopov. Nac. akad. nauk Ukr. 2017, 5:8-16|
The questions of solvability and determination of the coefficients of a nonlocal boundary-value problem for a second-order Fredholm integro-differential equation with degenerate kernel and reflecting deviation are conside red. The system of algebraic equations is obtained. Some features arising in the determination of the arbitrary (unknown) constants are removed. The criterion of one-value solvability of the considered problem is establi shed. Under this criterion, the one-valued solvability of the problem is proved, and the appropriate therem is proved.
|Keywords: degenerate kernel, integral condition, integro-differential equation, inverse boundary-value problem, one-valued solvability|
- Bang, N. D., Chistyakov, V. F. & Chistyakova, E. V. (2015). About some properties of degenerate systems of linear integro-differential equations. I. Izv. Irkutskogo gos. univ. Ser. Matem., 11, pp. 13-27 (in Russian).
- Bykov, Ja. V. (1957). On some problems of the theory of integro-differential equations. Frunze: Izd-vo Kirg. un-ta (in Russian).
- Vajnberg, M. M. (1964). Integro-differential equations. Itogi nauki. Ser. Mat. anal. Teor. veroyatn. Regulir. 1962. Moscow: VINITI, pp. 5-37 (in Russian).
- Vasil'jev, V. V. (1961). On the solution of the Cauchy problem for a class of linear integro-differential equations. Izv. Vyssh. Uchebn. Zaved. Mat., No. 4, pp. 8-24 (in Russian).
- Vlasov, V. V. & Perez Ortiz R. (2015). Spectral analysis of integro-differential equations in viscoelasticity and thermal physics. Mat.Notes, 98, Iss. 3, pp. 689-693. https://doi.org/10.1134/S0001434615090357
- Lando, Yu. K. (1961). A boundary-value problem for linear integro-differential equations of Volterra type in the case of disjoint boundary conditions Izv. Vyssh. Uchebn. Zaved. Mat., No. 3, pp. 56-65 (in Russian).
- Phalaleev, M. V. (2012). Integro-differential equations with Fredholm operator by the derivative of the higest order in Banach spaces and it's applications. Izv. Irkutskogo gos. univ. Ser. Matem., 5, No. 2, pp. 90-102 (in Russian).
- Gordeziani, D. G. & Avilishvili, G. A. (2000). On the constructing of solutions of the nonlocal initial boun dary value problems for one-dimensional medium oscillation equations. Matem. Modelirovanie, 12, No. 1, pp. 94-103 (in Russian).
- Ivanchov, N. I. (2004). Boundary value problems for a parabolic equation with integral conditions. Differ. Uravn., 40, No 4. pp. 547-564 (in Russian). https://doi.org/10.1023/B:DIEQ.0000035796.56467.44
- Tikhonov, I. V. (2003). Uniqueness theorems for linear non-local problems for abstract differential equations. Izv. RAN. Ser. Mat., 67, No. 2, pp. 133-166 (in Russian). https://doi.org/10.1070/IM2003v067n02ABEH000429
- Dzhumabaev, D. S. & Bakirova, E. A. (2015). On unique solvability of a boundary-value problem for Fredholm intergo-differential equations with degenerate kernel. Nonlinear Oscillations, 18, No. 4, pp. 489-506 (in Russian).
- Yuldashev, T. K. (2015). On Fredholm partial integro-differential equation of the third order. Izv. Vyssh. Uchebn. Zaved. Mat., No. 9, pp. 74-79 (in Russian). https://doi.org/10.3103/s1066369x15090091
- Yuldashev, T. K. (2016). Inverse problem for a nonlinear Benney—Luke type integro-differential equations with degenerate kernel. Izv. Vyssh. Uchebn. Zaved. Mat., No. 9, pp. 59-67 (in Russian). https://doi.org/10.3103/s1066369x16090061
- Yuldashev, T. K. (2016). Nonlocal mixed-value problem for a Boussinesq-type integrodifferential equation with degenerate kernel. Ukr. Math. Zh., 68, No. 8, pp. 1115-1131 (in Russian).