Solvability of A Nonlocal Problem By A Novel Concept of Fundamental Function

Abstract

Cauchy function, Green function and Riemann function are the several of the fundamental functions used frequently in the expression of a fundamental solution in the literature. In order to construct such functions, various ideas can be considered. The lesser-known one of these ideas is contained in the papers [1-4] by Seyidali S. Akhiev. Inspired by these papers, the solvability of some problems [12, 14, 15, 17-19] has been investigated. In this work, a novel kind of adjoint problem for a generally nonlocal problem, and also Green's functional via the solvability of that adjoint problem are constructed [21]. By means of the obtained Green's functional, an integral representation for the solution of the nonlocal problem is established.(1)