Existence of positive solution of the equation $$(-\Delta )^{s}u+a(x)u=|u|^{2^{*}_{s}-2}u$$ ( - Δ ) s u + a ( x ) u = | u | 2 s ∗ - 2 u

Abstract

In this paper we show existence of positive solution to the problem Open image in new window In order to prove the main result, we study a limit problem of (P). More precisely, we study the case when \(a=0\). Moreover, we prove the version to \({\mathbb {R}}^{N}\) of Struwe’s Global compactness result [14] for fractional Laplace operator.