**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 [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.

**Mathematics Subject Classification:**
34B05, 34B15

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