Existence results for a class of nonlocal problems involving p(x)-Laplacian

Abstract

We study the existence of weak solutions for a p(x)-Kirchhoff problem. The main tool used is the variational method, more precisely, the Mountain Pass Theorem. Mathematics Subject Classification 35J48 · 35J66

Existence results of a nonlocal superlinear problems Involving $p(x)-$Laplacian near to zero

“…They have introduced the asymptotic stability, as time tends to infinity. This type of Kirchhoff problems with stationary process has received considerable attention by several researchers, see for example [1,2,3,4,6,5,8,12,14,17,18,19] and the references therein. We consider the following nonlocal problem…”

Multiple Solutions for a Class of (P1(x), P2(x))-Laplacian Problems With Neumann Boundary Conditions

“…Very recently, Allaoui et al [2] have studied a class of nonlocal problems involving this type of operators. Motivated by the papers mentioned above, we study the existence of mutiple solutions for Neumann nonlinear problem (1) by using variational methods.…”