Ground state solutions for a class of elliptic Dirichlet problems involving the p(x)-Laplacian

We are interested in the existence and multiplicity of ground state solutions for a class of p(x)-Laplacian Dirichlet problem in bounded domains. Firstly, combining constraint variational method and quantitative deformation lemma, we prove that the equation possesses at least one least energy sign-changing solution with exactly two nodal domains. Finally, using a strong maximum principle, we obtain three ground state solutions (one positive, one negative, and one sign-changing) for this problem.