Infinitely many dichotomous solutions for the Schrödinger-Poisson system

In this paper, we consider the following Schrödinger-Poisson system where ε is a small parameter, , N ∈ [3, 6], and V ( x ) and K ( x ) are potential functions with different decay at infinity. We first prove the non-degeneracy of a radial low-energy solution. Moreover, by using the non-degenerate solution, we construct a new type of infinitely many solutions for the above system, which are called “dichotomous solutions”, i.e., these solutions concentrate both in a bounded domain and near infinity.