On Nonlocal Elliptic Systems of p(x)-Kirchhoff-Type under Neumann Boundary Condition

摘要

This paper is concerned with the existence of solutions to a class of p(x)-Kirchhofftype systems under Neumann boundary condition.By Ekeland Variational Principle and the theory of the variable exponent Sobolev spaces,we establish conditions ensuring the existence of solutions for the problem.Since the Poincaré's inequality does not hold in the space W1,p(x) (Ω),we shall prove the Poincaré-Wirtinger's inequality in a subspace of W1,p(x)(Ω).