An existence result for super-critical problems involving the fractional [formula omitted]-Laplacian in [formula omitted

Abstract

In this paper we establish an existence result for the following super-critical problems involving the fractional p-Laplacian (−Δ)psu+V(x)|u|p−2u=|u|ς−2u+λ|u|q−2u,inRN,where 0<s<1, 1<q<p<ς and sp<N. Here the nonlinearity |u|ς−2u imposes no any growth conditions. This is a new result for super-critical values of ς.