The Existence and Multiplicity of Solutions for p x -Laplacian-Like Neumann Problems

Abstract

In the present paper, in view of the variational approach, we discuss the Neumann problems with $p\left(x\right)$ -Laplacian-like operator and nonstandard growth condition, originated from a capillary phenomena. By using the least action principle and fountain theorem, we prove the existence and multiplicity of solutions to the class of Neumann problems under suitable assumptions.