In the present paper, by using the direct variational method and the Ekeland variational principle, we study the existence of solutions for an elliptic system of p(x)-Kirchhoff-type under Neumann boundary condition and show the existence of a weak solution.

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 W ,p(x) (Ω), and the main tools are the Mountain-Pass theorem and Fountain theorem.

In this paper, using the Nehari manifold approach and some variational techniques, we discuss the multiplicity of positive solutions for the p(x)-Laplacian problems with non-negative weight functions and prove that an elliptic equation has at least two positive solutions.

This paper investigates the existence and multiplicity of solutions for superlinear p(x)-Laplacian equations with Dirichlet boundary conditions. Under no Ambrosetti-Rabinowitz's superquadraticity conditions, we obtain the existence and multiplicity of solutions using a variant Fountain theorem without Palais-Smale type assumptions.

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