Non-local problems with an integral condition for third-order differential equations

Abstract

The paper is devoted to the study of the solvability of nonlocal problems with an integral variable $t$ condition for the equations $$u_{tt}+(\alpha\frac{\partial}{\partial t}+\beta)\Delta u=f(x,t)$$($\alpha$, $\beta$ are valid constants, $\Delta$ is Laplace operator by spatial variables). Theorems are proved for the studied problems existence and non-existence, uniqueness and non-uniqueness solutions (having all derivatives generalized by S. L. Sobolev included in the equation).

Keywords

• third-order differential equations
• non-local problems
• integral conditions
• regular solutions
• uniqueness
• existence