Least energy sign-changing solutions for the fractional Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$

Abstract

Abstract In this paper, we study the following nonlinear fractional Schrödinger–Poisson system 0.1 {(−Δ)su+V(x)u+ϕu=K(x)f(u),x∈R3,(−Δ)tϕ=u2,x∈R3. $$ \textstyle\begin{cases} (-\Delta )^{s}u+V(x)u+\phi u=K(x)f(u),&x\in \mathbb{R}^{3}, \\ (-\Delta )^{t} \phi =u^{2},&x\in {\mathbb{R}}^{3}. \end{cases} $$ where s∈(34,1) $s\in (\frac{3}{4},1)$, t∈(0,1) $t\in (0,1)$, V,K:R3→R $V,K : \mathbb{R}^{3}\rightarrow \mathbb{R}$ 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.

Keywords

• Fractional Schrödinger–Poisson systems
• Constraint variational methods
• Quantitative deformation lemma
• Sign-changing solution
• Zero mass