Onpz–Laplacian System Involving Critical Nonlinearities

Abstract

In this paper, we deal with the existence of at least two nonnegative nontrivial solutions to apz–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.