Existence of Nontrivial Weak Solutions for a Class of p & q Elliptic Problem with Discontinuous Nonlinearity and Critical Exponent

Abstract

In this work, we will study a quasilinear problem with critical exponent and two different kinds of discontinuous nonlinearity. By applying the critical point theory for nondifferentiable functionals, we will prove that our problem has at least one nontrivial weak solution for any value of positive parameters associated with the problem. We proved new results when one of the nonlinearities satisfied the Ambrosetti-Rabinowitz (AR) condition.