Investigating the multiplicity and concentration behaviour of solutions for a quasi-linear Choquard equation via the penalization method (Q2799609)

The authors consider the quasilinear Choquard equation, which involves the \(p\)-Laplacian operator and a general nonlinear term (instead of the Laplacian and a power-type nonlinear term). Under the hypothesis that the potential function has a local minimum, they prove the existence, multiplicity and concentration behaviour of positive solutions for the equation. The approach is based on the penalization method and the Lyusternik-Schnirelmann category theory (for proving the multiplicity result) and on the Moser iteration method (for studying the concentration behaviour). The results are new even for the semilinear case \(p=2\).