Well-posedness of a problem with initial conditions for hyperbolic differential-difference equations with shifts in the time argument

We study a problem with initial conditions on the half-line for a differentialdifference equation of the hyperbolic type with deviations of the time argument. We obtain sufficient conditions for the well-posed solvability of the problem in Sobolev spaces with an exponential weight. In terms of the spectrum of the problem operator, we obtain necessary conditions for the well-posed solvability of the problem, sufficient conditions for the absence of solutions, and sufficient conditions for the nonuniqueness of the solution. © 2016, Pleiades Publishing, Ltd.

Авторы
Akbari Fallahi A. , Yaakbarieh A. 1, 2 , Sakbaev V.Z. 1, 2
Журнал
Номер выпуска
3
Язык
Английский
Страницы
346-360
Статус
Опубликовано
Том
52
Год
2016
Организации
  • 1 Peoples’ Friendship University of Russia, Moscow, Russian Federation
  • 2 Moscow Institute of Physics and Technology, Moscow, Russian Federation
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