On a Nonlocal Problem for the Nonhomogeneous Boussinesq Type Integro-Differential Equation with Degenerate Kernel

Abstract

This paper considers the questions of solvability and constructing the solution of a nonlocal boundary value problem for the fourth-order Boussinesq type nonhomogeneous partial integro-differential equation with degenerate kernel. The Fourier method based on separation of variables has been used. The system of algebraic equations has been obtained. The criterion of unique solvability of the considered problem has been revealed. The theorem of solvability of the problem has been proved under this criterion.

Keywords

• integro-differential equation
• boundary value problem
• degenerate kernel
• integral conditions
• solvability