IJPAM: Volume 113, No. 4 (2017)

Title

SOLVABILITY AND CONSTRUCTION OF A SOLUTION
OF THE BOUNDARY VALUE PROBLEM FOR LINEAR
INTEGRAL AND DIFFERENTIAL EQUATIONS
WITH RESTRICTIONS

Authors

Serikbai A. Aisagaliev$^1$, Sofiya S. Aisagalieva$^2$
$^{1,2}$Al-Farabi Kazakh National University
Almaty, KAZAKHSTAN

Abstract

The necessary and sufficient conditions for the solvability of boundary value problems for linear integral - differential equations with phase and integral constraints are obtained. The method of constructing the solution of the boundary value problem with constraints is developed by constructing minimizing sequences. The base of the proposed method for solving the boundary value problem is the principle of immersion. The principle of immersion has been created by building the general solution of a class of Fredholm integral equations of the first kind.

History

Received: December 15, 2016
Revised: January 30, 2017
Published: March 30, 2017

AMS Classification, Key Words

AMS Subject Classification: 35C15, 35E15, 35K05, 35K20
Key Words and Phrases: constructive theory, boundary value problems, linear integro-differential equations, the principle of immersion

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Bibliography

1
Ja.V. Bykov, Some problems of integral-differential equations, Frunze (1957).

2
A.M. Samoilenko, O.A. Bojchuk, S.A. Krivosheja,Boundary value problems for systems of the linearintegral-differential equations with degenerate kernel, Ukr.math. journal, 48, No. 11 (1996), 1576-1579.

3
D.S. Dzhumabaev, E.A. Bakirova, About properties ofsolvability of the linear twopoint boundary value problem forsystems of the integral-differential equations, Differentialequations, 49, No. 9 (2013), 1125-1140.

4
S.A. Aisagaliev, Constructive theory of the boundary valueproblems of integral-differential equations with phaseconstraints, Bulletin of Kyrgyz state national university.Ser. 3, No. 4 (2000), 127-133.

5
S.A. Aisagaliev, T.S. Aisagaliev, Methods of solution of theboundary value problems, Kazakh university, Almaty (2002).

6
S.A. Aisagaliev, Control by some system of differential equations,Differetial equations, 27, No.9 (1991), 1475-1486.

7
S.A. Aisagaliev, A.P. Belogurov, Controllability and speed of theprocess described by parabolic equation with limited control, mathematical journal, 53, No. 1 (2012), 20-37.

8
S.A. Aisagaliev, General solution of a class integral equations,Mathematical journal, 5, No. 4 (2005), 7-13.

9
S.A. Aisagaliev, A.A. Kabidoldanova, Optimal control by linearsystems with linear quality criteria and restrictions, equations, 48, No. 6 (2012), 826-838.

10
S.A. Aisagaliev, M.N. Kalimoldaev, Constructive method forsolution of the boundary value problems for ordinary differentialequations, Differetial equations, 51, No. 2 (2015),147-160.

11
R. Kalman, On general theory of control systems, Proceedingsof the i-st congress IFAK, Moscow, 2 (1961), 521-547.

12
A.N. Kolmogorov, S.V. Fomin, Elements of the function theoryand functional analysis, Nauka, Moscow (1989).

13
S.A. Aisagaliev, S.S. Aisagalieva, Solvability and construction ofa solution of the boundary value problem for linear integral anddifferential equations with restrictions, Kazakh MathematicalJournal, 17, No. 1 (2017), 24-25.

How to Cite?

DOI: 10.12732/ijpam.v113i4.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 4
Pages: 17 - 29


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