Existence and concentration of nontrivial solutions for a fractional magnetic Schrödinger-Poisson type equation

Vincenzo Ambrosio
2019 Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V  
We consider the following fractional Schrödinger-Poisson type equation with magnetic fields a positive continuous electric potential and f : R ! R is a continuous function with subcritical growth. Using suitable variational methods, we show the existence of a family of nontrivial solutions which concentrates around global minima of the potential V (x) as " ! 0. Mathematics Subject Classification (2010): 35A15 (primary); 35R11, 35S05 (secondary).
doi:10.2422/2036-2145.201804_022 fatcat:y7vla3e6cjblrdmh7f3jvayyva