Fractional p-Laplacian Problem with Critical Stein-Weiss Type Term

The paper is concerned with the p-Laplacian minimizing problem with critical Stein-Weiss type term, and a nonlocal nonlinear equation involving fractional p-Laplacian operator and critical Stein-Weiss type term. Then main difficulty is hard to get the compactness of bounded minimizing sequence (and bounded Palais-Smale sequence). By the refined Sobolev inequality with Lorentz norm, we establish a abstract theorem, which is the relatively compactness result of bounded symmetric decreasing sequence. And then, as applications, we prove the existence, decay and regular results for the problems.