|
This article is cited in 1 scientific paper (total in 1 paper)
Differentical equations, dynamical systems and optimal control
Nonlocal problems with an integral boundary condition for the differential equations of odd order
A. I. Kozhanovab, G. A. Lukinac a Novosibirsk State University, ul. Pirogova, 2, 630090, Novosibirsk, Russia
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
c Mirny Polytechnic Institute (branch) of Ammosov North-Eastern Federal University, ul. Tikhonova, 5 korp. 1, 678170, Mirny, Russia
Abstract:
We study the solvability of nonlocal problems for equations $$u_{ttt} + Au=f(x,t)$$
($0<T<+\infty$, $A$ — elliptic operator) with only two boundary conditions instead of three and with a special integral boundary condition. We prove the existence theorems for regular solutions and indicate a possible generalization of the obtained results.
Keywords:
nonlocal problem, integral condition, odd order differential equation, regular solution, existence.
Received February 22, 2016, published June 1, 2016
Citation:
A. I. Kozhanov, G. A. Lukina, “Nonlocal problems with an integral boundary condition for the differential equations of odd order”, Sib. Èlektron. Mat. Izv., 13 (2016), 452–466
Linking options:
https://www.mathnet.ru/eng/semr689 https://www.mathnet.ru/eng/semr/v13/p452
|
|