EXISTENCE OF POSITIVE SOLUTIONS FOR A GENERALIZED FRACTIONAL BREZIS-NIRENBERG PROBLEM

In this article, we study the fractional Bre<acute accent>zis-Nirenb erg type problem on whole domain RN associated with the fractional p-Laplace operator. To be precise, we want to study the following problem: (P) (-Delta p)su - lambda w|u|p-2u = |u|p & lowast;s -2u in Ds,p(RN), where s is an element of (0, 1), p is an element of (1, N/s), p & lowast;s = Np/(N - sp) and the operator (-Delta p)s is the fractional p-Laplace operator. The space Ds,p(RN) is the completion of C infinity (RN) with respect to the Gagliardo semi-norm. In this article, we c prove the existence of a positive solution to problem (P) by allowing the Hardy weight function w to change its sign.