Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear terms
Abstract In this paper, we study the following fractional Schrödinger–Poisson system with superlinear terms {(−Δ)su+V(x)u+K(x)ϕu=f(x,u),x∈R3,(−Δ)tϕ=K(x)u2,x∈R3, $$ \textstyle\begin{cases} (-\Delta )^{s}u+V(x)u+K(x)\phi u=f(x,u), & x \in \mathbb{R}^{3}, \\ (-\Delta )^{t}\phi =K(x)u^{2}, & x \...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-01-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1121-4 |
| Summary: | Abstract In this paper, we study the following fractional Schrödinger–Poisson system with superlinear terms {(−Δ)su+V(x)u+K(x)ϕu=f(x,u),x∈R3,(−Δ)tϕ=K(x)u2,x∈R3, $$ \textstyle\begin{cases} (-\Delta )^{s}u+V(x)u+K(x)\phi u=f(x,u), & x \in \mathbb{R}^{3}, \\ (-\Delta )^{t}\phi =K(x)u^{2}, & x \in \mathbb{R}^{3}, \end{cases} $$ where s,t∈(0,1) $s,t\in (0,1)$, 4s+2t>3 $4s+2t>3$. Under certain assumptions of external potential V(x) $V(x)$, nonnegative density charge K(x) $K(x)$ and superlinear term f(x,u) $f(x,u)$, using the symmetric mountain pass theorem, we obtain the existence and multiplicity of non-trivial solutions. |
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| ISSN: | 1687-2770 |