Solutions of Nonlocal -Laplacian Equations

Abstract

In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving ( 1 ( ), 2 ( ))-Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.

Existence of solutions for a nonlocal (P_1(x), P_2(x))-Laplace equation with dependence on the gradient

“…In [32,33,42,47] the authors consider the problem (1.1), with M 1 = M 2 = 1 , p 1 = p 2 ; p 1 , p 2 continuous functions and f = f (x, u), they showed existence of solutions via variational methods. As far as we know, there is few papers that deals with nonlocal problem involving (p 1 (x), p 2 (x)) Laplace operator (see [3]).…”