Abildayeva, A. D. Kaparova, R. M. Assanova, A. T.
Published in
Lobachevskii Journal of Mathematics

AbstractProblem with integral condition for Fredholm integro-differential equation is considered. Conditions for a unique solvability of problem with integral condition for Fredholm integro-differential equation are established by method of introducing parameter. Results are illustrated to problem for Fredholm integro-differential equation with int...

Usmanov, K. I. Nazarova, K. Zh. Yerkisheva, Zh. S.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper, we consider a boundary value problems for a systems of loaded integro-differential equations with an involutory transformation. The parameterization method is applied to the boundary value problem for a system with continuous kernel. By using the properties of involutory transformation, the problem is transformed to a boundar...

Zakora, D. A.
Published in
Lobachevskii Journal of Mathematics

AbstractIn this paper, we consider the hyperbolic thermoelastic system of memory type and the corresponding system of abstract integro-differential equations. We study forced motions of this system of abstract integro-differential equations and investigate the asymptotic behavior of solutions to this system as time goes to infinity.

Mamedov, Kh. R.
Published in
Lobachevskii Journal of Mathematics

AbstractWe considered the mixed parabolic-hyperbolic type equation with discontinuous coefficient in a rectangular domain.We established a criterion for the unique solvability of this problem,using this criterion constructed solution as the sum of Fourier series. Finally, the stability of the solution with respect to initial function is proved.

Assanova, A. T.
Published in
Lobachevskii Journal of Mathematics

AbstractTwo-point boundary value problem for fourth order partial integro-differential equation is considered. By new unknown function the problem is reduced to an equivalent family of two-point boundary value problems for the Volterra integro-differential equations of second order. By the method of introduction functional parameters are constructe...

Assanova, A. T. Dzhobulaeva, Zh. K. Imanchiyev, A. E.
Published in
Lobachevskii Journal of Mathematics

AbstractMulti-point initial boundary value problem for fourth order system of partial differential equations is considered. By new unknown function the problem is reduced to an equivalent nonlocal problem for system of hyperbolic equations of second order with dynamical condition. By the method of introduction functional parameters are constructed ...

Glushak, A. V.
Published in
Lobachevskii Journal of Mathematics

AbstractA family of singular differential equations with variable coefficients and parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\in\mathbb{R}$$\end{docume...

Assanova, A. T. Imanchiyev, A. E. Kadirbayeva, Zh. M.
Published in
Russian Mathematics

We consider a nonlocal problem for a system of loaded differential equations of the Sobolev type with a multipoint constraint. By introducing additional unknown functions, we reduce the problem under consideration to an equivalent problem consisting of a nonlocal multipoint problem for a system of loaded hyperbolic equations of the second order wit...

Petrova, A. G.
Published in
Mathematical Notes

We consider the boundary-value problem in a semibounded interval for a fourth-order equation with “double degeneracy”: the small parameter in the equation multiplies the product of the unknown function vanishing on the boundary and its highest derivative. Such a problem arises in the description of the motion of weak solutions of polymers near a cr...

Glushak, A. V.
Published in
Russian Mathematics

We find sufficient conditions for the unique solvability of nonlocal problem for the abstract Bessel—Struve differential equation. Both nonlocal conditions are written with the help of Krdelyi—Kober operators.