Least energy sign-changing solutions for the fractional Schrödinger–Poisson systems in R 3 $\mathbb{R}^{3}$

Abstract

In this paper, we study the following nonlinear fractional Schrödinger-Poisson system (-) s u + V(x)u + φu = K(x)f (u), x ∈ R 3 , (-) t φ = u 2 , x ∈ R 3. (0.1) where s ∈ (3 4 , 1), t ∈ (0, 1), V, K : R 3 → R are continuous functions verifying some conditions about zero mass. By using the constraint variational method and the quantitative deformation lemma, we obtain the existence of least energy sign-changing solution to this system.

Multiple solutions for a class of fractional logarithmic Schrödinger equations

“…Thus we define a new set M, which is different from the case of local operator [28]. This idea comes from the work in [29].…”

“…By a minimization argument and a quantitative deformation lemma, Ambrosio and Isernia [3] obtained the existence of a sign-changing solution when the potential vanishes at infinity. Wang et al [29] used constraint variational method and quantitative deformation lemma to get the existence of least energy sign-changing solutions to the nonlinear fractional Schrödinger-Poisson systems. For some other results about signchanging solutions, see [2,17,23,31].…”

Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R 3 $\mathbb{R}^{3}$

“…For the other work on a sign-changing solution of system (1.5) or similar problems, we refer the reader to [5,20,21,27,30,56,68] and the references therein. It is noticed that there are some interesting results, for example [10,13,53,61], considered sign-changing solutions for other nonlocal problems.…”

Positive bound state solutions for the nonlinear Schrödinger–Poisson systems with potentials

“…In recent years, several scholars paid their attention to the existence of positive, ground state, semiclassical, and other solutions to fractional Schrödinger-Poisson system or similar problems. For the information, one can refer to [21][22][23][27][28][29] and the references therein. However, it is worth to point out that in most of the papers mentioned above, the study involves positive ground state solutions to (1.1).…”