ON COMPUTATION OF EIGENFUNCTIONS OF
COMPOSITE TYPE EQUATIONS WITH
REGULAR BOUNDARY VALUE CONDITIONS
Nurlan S. Imanbaev1,2, Yeleu Kurmysh2
1Institute of Mathematics and Mathematical Modeling
Str. Pushkin 125, 050010 - Almaty, KAZAKHSTAN
2Department of Mathematics
South Kazakhstan State Pedagogical University
Str. Baitursynov 13, 160000 - Shymkent, KAZAKHSTAN

Abstract

In this paper, we consider the question on computation of eigenvalues and eigenfunctions of a third-order composite type equation in a rectangular region $D$ of the space $W_2^3\left( {0, 1} \right)$ satisfying the following boundary conditions

\begin{displaymath}{\left. u \right\vert _{\partial D}} = 0, \quad {u_x}\left( {... ... \quad {u_y}\left( {x, 0} \right) = {u_y}\left( {x, 1} \right),\end{displaymath}

where $D = \left\{ {x, y: 0 < x < 1, 0 < y < 1} \right\}$. All eigenvalues and eigenfunctions of the considered spectral problem are found, and the adjoint operator is constructed.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 4
Year: 2021

DOI: 10.12732/ijam.v34i4.7

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