INFINITELY MANY SOLUTIONS FOR NONLOCAL SYSTEMS INVOLVING FRACTIONAL LAPLACIAN UNDER NONCOMPACT SETTINGS

摘要

In this paper, we study a class of Brezis-Nirenberg problems for nonlocal systems, involving the fractional Laplacian (-Delta)(s) operator, for 0 < s < 1, posed on settings in which Sobolev trace embedding is noncompact. We prove the existence of infinitely many solutions in large dimension, namely when N > 6s, by employing critical point theory and concentration estimates.