Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2000; 37(6): 1031-1042

Printed November 1, 2000

Copyright © The Korean Mathematical Society.

On the boundary value problems for loaded differential equations

Muvasharkhan T. Dzhenaliev

Abstract

The equations prescribed in $\Omega\subset\mathbb{R}^n$ are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than $n$) from closure $\bar{\Omega}$. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.

Keywords: Evolution equation, loaded differential equation, boundary value problem

MSC numbers: 35D05, 34K06, 34K10