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

We prove the existence of infinitely many solutions to a fractional Choquard type equation $$(-\mathrm{\Delta }{)}_p^{s}u+V(x)\mathrm{\mid }u{\mathrm{\mid }}^{p-2}u=(K\ast g(u))g^{\mathrm{\prime }}(u)+{\epsilon }_{W}W(x)f^{\mathrm{\prime }}(u)\text{in }{\mathbb{R}}^N$$ 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.