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

Masaki Sakuma

Published 2023-05-02Version 1

We prove the existence of infinitely many solutions to a fractional Choquard type equation \[ (-\Delta)^s_p u+V(x)|u|^{p-2}u=(K\ast g(u))g'(u)+\varepsilon_W W(x)f'(u)\quad\text{in }\mathbb{R}^N \] involving 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 a sequence 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.