Ground state solutions for a class of nonlinear fractional Schrödinger–Poisson systems with super-quadratic nonlinearity

Existence of ground state solutions for an asymptotically 2-linear fractional Schrödinger–Poisson system

“…Remark 3.1 If s = t = 1, Our main result Theorem 3.1 reduces to Theorem 1.1 in [5]. On the other hand, Theorem 3.1 in this paper relaxes the condition of super-quadratic nonlinearity in [1] to being asymptotically 2-linear.…”

“…Yin, Wu and Tang [5] proved the existence of ground state solutions of (1.2) by using Inspired by [5], the main objective of this paper is to extend the main results of [1], by relaxing the condition of super-quadratic nonlinearity used in [1]. That is, the nonlinearity f is assumed to be asymptotically 2-linear.…”

“…In this paper, we study the existence of ground state solutions for the following fractional Schrödinger-Poisson system: In recent years, the nonlinear fractional Schrödinger-Poisson systems have received a lot of attention. In [1], Gao, Tang and Chen studied the existence of ground state solutions of (1.1) in a mild assumption on f with super-quadratic nonlinearity. If u is replaced by V (x)u and f (u) = μ|u| q-2 u+|u| 2 * s -2 u (2 * s = 6 3-2s ) in (1.1), the existence of a nontrivial ground state solution is given by Teng [2].…”

Fractional Schrödinger–poisson System With Singularity: Existence, Uniqueness, and Asymptotic Behavior

“…Li et al [21] studied the existence of infinitely many solutions for a fractional Schrödinger-Poisson-Kirchhoff type system in the subcritical and critical case. For more works on fractional Schrödinger-Poisson system, one can see [7,30,37] and the references cited therein.…”

“…, see, for example, [7,21] or Section 2 of this article. Inserting this φ t u into the first equation of the system…”