Infinitely many solutions for p-fractional Choquard type equations involving general nonlocal nonlinearities with critical growth via the concentration compactness method

Abstract

We prove the existence of infinitely many solutions to a fractional Choquard type equation(−Δ)psu+V(x)|u|p−2u=(K⁎g(u))g′(u)+εWW(x)f′(u)in RN involving the fractional p-Laplacian and a general convolution term with critical growth. In order to obtain infinitely many solutions, we use a type of the symmetric mountain pass lemma which gives sequences of critical values converging to zero for even functionals. To assure the (PS)c conditions, we also use a nonlocal version of the concentration compactness lemma.