# Solvability of a two-point boundary value problem with phase and integral constraints

### Abstract

New mathematical techniques for considering the complex boundary value problems to solve topical problems of natural sciences, technology, economy and ecology etc. are needed. Mathematical models of nuclear and chemical reactors management processes, control of electric power and robotic systems, economic management and others are complex boundary value problems of ordinary differential equations. Boundary value problems are called complex if besides the boundary conditions there exist the phase constraints and integral constraints on the phase coordinates of the system. The main objectives are: the necessary and sufficient conditions for the existence of solutions of boundary value problems and the methods of construction of complex solutions of boundary value problems. The aim of the work is an attempt to create a unified theory of the study of solvability of boundary value problems and the construction of a general method for solving them, based on the use of modern computer technology. The work is devoted to solving the problems of boundary value problems of nonlinear systems of ordinary differential equations. We consider the boundary value problem with boundary conditions of the given convex closed sets. The necessary and sufficient conditions for existence of a solution of the problem and construction its solution are obtained. The basis of the proposed method for solving of the boundary value problem is a possibility to reduce to a class of linear Fredholm integral equation of the first kind [1]-[9]. Necessary and sufficient condition for existence of a solution of integral equation is proved. Fredholm integral equation of the first kind belongs to the insufficiently explored problems in mathematics [11]- [22].Закрыть

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Казахский

Китайский Трад

Китайский Упр

Корейский

Русский

Турецкий

Французский

Английский

Испанский

Итальянский

Казахский

Китайский Трад

Китайский Упр

Корейский

Русский

Турецкий

Французский

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How to Cite

AISAGALIEV, S.; ZHUNUSSOVA, Zh.; AKCA, H..
Solvability of a two-point boundary value problem with phase and integral constraints.

**International Journal of Mathematics and Physics**, [S.l.], v. 8, n. 1, p. 4-12, june 2017. ISSN 2409-5508. Available at: <https://ijmph.kaznu.kz/index.php/kaznu/article/view/216>. Date accessed: 02 dec. 2022. doi: https://doi.org/10.26577/ijmph.2017.v8.i1.01.
Section

MATHEMATICS