J. Korean Math. Soc. 2000; 37(6): 1031-1042
Printed November 1, 2000
Copyright © The Korean Mathematical Society.
Muvasharkhan T. Dzhenaliev
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
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