Kemal Özen

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  [14] by Seyidali S. Akhiev. Inspired by these papers, the solvability of some problems  [12,14,15,1719] 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.

Mathematics Subject Classification: 34B05, 34B15

Key words and phrases: Second order ordinary differential equation, linear, nonlinear, the Neumann problem, existence theorem, uniqueness theorem