Nonlocal Integro-Differential Equations of the Second Order with Degeneration

Abstract

We study the solvability for boundary value problems to some nonlocal second-order integro–differential equations that degenerate by a selected variable. The possibility of degeneration in the equations under consideration means that the statements of the corresponding boundary value problems have to change depending on the nature of the degeneration, while the nonlocality in the equations implies that the boundary conditions will also have a nonlocal form. For the problems under study, the paper provides conditions that ensure their well-posedness.

Keywords

• integro-differential equation
• degeneration
• boundary value problem
• non-local conditions
• well-posedness