Existence of solutions of integro-differential semilinear elliptic equations

ABSTRACT

In this paper, we focus our attention on the equation (1) $-div(a(x)\mathrm{\nabla }u(x))+\eta \psi (x){\int }_{\mathrm{\Omega }}\phi u=f(x,u)\mathrm{in}\mathrm{\Omega },u=0\mathrm{on}\mathrm{\partial }\mathrm{\Omega }$(1) for which we get nontrivial solutions for some classes of functions f, where $\mathrm{\Omega }\subset {\mathbb{R}}^N$, $N\ge 1$, is a bounded smooth domain and a, ψ, φ, f are functions whose properties will be timely introduced.

KEYWORDS:

• Non-local problems
• variational methods
• integral operators
• elliptic equations

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 35A15
• 45P05

Disclosure statement

No potential conflict of interest was reported by the author(s).