Existence of positive solutions for a class of p& q elliptic problem with critical exponent and discontinuous nonlinearity

Abstract

In this paper we study the existence of positive solutions to a class of p& q elliptic problems given by -div(a(|∇u|p)|∇u|p-2∇u)=f(u)+|u|q∗-2uinΩ,u=0on∂Ω,where Ω ⊂ R N is bounded, 2 ≤ p≤ q< q ∗ , f: R→ R is a function that can have an uncountable set of discontinuity points and the function a is a continuous function. This result to extend previous ones to a larger class of p& q type problems.