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, $$ \textstyle\begin{cases} (-\Delta )^{s}u+V(x)u+K(x)\phi u=f(x,u), & x \in \mathbb{R}^{3}, \\ (-\Delta )^{t}\phi =K(x)u^{2}, & x \...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2019-01-01
|
| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1121-4 |
| _version_ | 1818535658536304640 |
|---|---|
| author | Yan He Lei Jing |
| author_facet | Yan He Lei Jing |
| author_sort | Yan He |
| collection | DOAJ |
| description | Abstract In this paper, we study the following fractional Schrödinger–Poisson system with superlinear terms {(−Δ)su+V(x)u+K(x)ϕu=f(x,u),x∈R3,(−Δ)tϕ=K(x)u2,x∈R3, $$ \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} $$ where s,t∈(0,1) $s,t\in (0,1)$, 4s+2t>3 $4s+2t>3$. Under certain assumptions of external potential V(x) $V(x)$, nonnegative density charge K(x) $K(x)$ and superlinear term f(x,u) $f(x,u)$, using the symmetric mountain pass theorem, we obtain the existence and multiplicity of non-trivial solutions. |
| first_indexed | 2024-12-11T18:27:51Z |
| format | Article |
| id | doaj.art-676f8b5121884038879660b0a8c24a72 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-11T18:27:51Z |
| publishDate | 2019-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-676f8b5121884038879660b0a8c24a722022-12-22T00:55:00ZengSpringerOpenBoundary Value Problems1687-27702019-01-012019111010.1186/s13661-019-1121-4Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear termsYan He0Lei Jing1School of Statistics and Mathematics, Zhongnan University of Economics and LawSchool of Mathematical Sciences, Capital Normal UniversityAbstract In this paper, we study the following fractional Schrödinger–Poisson system with superlinear terms {(−Δ)su+V(x)u+K(x)ϕu=f(x,u),x∈R3,(−Δ)tϕ=K(x)u2,x∈R3, $$ \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.http://link.springer.com/article/10.1186/s13661-019-1121-4Fractional Schrödinger–Poisson systemSymmetric Mountain Pass Theorem |
| spellingShingle | Yan He Lei Jing Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear terms Boundary Value Problems Fractional Schrödinger–Poisson system Symmetric Mountain Pass Theorem |
| title | Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear terms |
| title_full | Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear terms |
| title_fullStr | Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear terms |
| title_full_unstemmed | Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear terms |
| title_short | Existence and multiplicity of non-trivial solutions for the fractional Schrödinger–Poisson system with superlinear terms |
| title_sort | existence and multiplicity of non trivial solutions for the fractional schrodinger poisson system with superlinear terms |
| topic | Fractional Schrödinger–Poisson system Symmetric Mountain Pass Theorem |
| url | http://link.springer.com/article/10.1186/s13661-019-1121-4 |
| work_keys_str_mv | AT yanhe existenceandmultiplicityofnontrivialsolutionsforthefractionalschrodingerpoissonsystemwithsuperlinearterms AT leijing existenceandmultiplicityofnontrivialsolutionsforthefractionalschrodingerpoissonsystemwithsuperlinearterms |