On the nonlocal Schrödinger‐poisson type system in the Heisenberg group

Abstract

This paper is concerned with a class of nonlocal Schrödinger‐Poisson type system with sublinear term. With the aid of the Ekeland's variational principle and the mountain pass theorem, the existence of negative energy solution, positive energy solution, and positive ground state solution is obtained, respectively. Moreover, we also obtain the multiplicity of solutions by using the Clark theorem. The novelty of this paper is that the equation has not only nonlocal term but also nonlocal coefficient.