Abstract
The aim of this paper is to study a concentration-compactness principle for homogeneous fractional Sobolev space Ds,2(RN) for 0<s<min{1,N/2}. As an application we establish Palais–Smale compactness for the Lagrangian associated to the fractional scalar field equation (−Δ)su=f(x,u) for 0<s<1. Moreover, using an analytic framework based on Ds,2(RN), we obtain the existence of ground state solutions for a wide class of nonlinearities in the critical growth range.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have