Ground state solutions for the nonlinear fractional Schrodinger-Poisson system

Abstract

In this paper, we study the existence of ground state solutions for the nonlinear fractional Schrödinger-Poisson system \begin{equation*} \left\{ \begin{array}{ll} (-Δ)^su+V(x)u+ϕu=|u|^{p-1}u, & \hbox{in ${\mathbb{R}}^3$,} (-Δ)^sϕ=u^2,& \hbox{in ${\mathbb{R}}^3$,} \end{array} \right. \end{equation*} where $2<p<2_s^{\ast }-1=\frac{3+2s}{3-2s}$, $s\in (\frac{3}{4},1)$. Under certain assumptions on $V$, a nontrivial ground state solution $(u,\varphi )$ is established through using a monotonicity trick and global compactness Lemma. As its supplementary results, we prove some nonexistence results in the case of $1<p\le 2$ and $p=2_s^{\ast }-1$.

60pages. arXiv admin note: text overlap with arXiv:1305.6791 by other authors

References in corpus (5)

• Nonlocal diffusion and applications
• Existence and symmetry results for a Schrödinger type problem involving the fractional Laplacian
• Fractional elliptic problems with critical growth in the whole of ${\mathbb{R}}^n$
• Ground states for fractional magnetic operators
• Fractional Schrödinger-Poisson systems with a general subcritical or critical nonlinearity

Cited by in corpus (2)

• Concentrating phenomenon for fractional nonlinear Schrödinger-Poisson system with critical nonlinearity
• Bound state solutions for non-autonomous fractional Schrödinger-Poisson equations with critical exponent