Vortex-type solutions for magnetic pseudo-relativistic Hartree equation

Abstract

We deal with a class of magnetic pseudo-relativistic Hartree type equation where , m>0, is a continuous vector potential, is an external continuous scalar potential and is a convolution kernel, is a positive constant, , . Under the action of some subgroup of linear isometries on potential A and W, and some assumptions on the decay of A and W at infinity, we prove the existence of vortex-type solutions to this problem by using variational methods and asymptotic estimates as p = 2.