Solutions of nonlinear problems involving p(x)-Laplacian operator

Abstract

In the present paper, by using variational principle, we obtain the existence and multiplicity of solutions of a nonlocal problem involving p(x)-Laplacian. The problem is settled in the variable exponent Sobolev space W01,p(x)(Ω), and the main tools are the Mountain-Pass theorem and Fountain theorem.

Keywords

• p(x)-laplacian
• nonlocal problem
• variational methods
• mountain pass theorem
• fountain theorem
• 35b30
• 35d05
• 35j60
• 35j70