On pz–Laplacian System Involving Critical Nonlinearities

Abstract

In this paper, we deal with the existence of at least two nonnegative nontrivial solutions to a pz–Laplacian system involving critical nonlinearity in the context of Sobolev spaces with variable exponents on complete manifolds. We have established our main results by exploring both Nehari’s method and doing a refined analysis on the associated fiber map and some variational techniques.