Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems
Abstract This paper deals with the following generalized nonhomogeneous Kirchhoff–Schrödinger–Poisson system: {(a+∫R3|∇u|2+b∫R3u2)(−Δu+bu)+qϕf(u)=g(u)+h(x),in R3,−Δϕ=2qF(u),in R3, $$ \textstyle\begin{cases} (a+\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}+b\int _{\mathbb{R}^{3}} u ^{2} )(-\Delta...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-08-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1252-7 |
| _version_ | 1828764085264580608 |
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| author | Hongxia Shi |
| author_facet | Hongxia Shi |
| author_sort | Hongxia Shi |
| collection | DOAJ |
| description | Abstract This paper deals with the following generalized nonhomogeneous Kirchhoff–Schrödinger–Poisson system: {(a+∫R3|∇u|2+b∫R3u2)(−Δu+bu)+qϕf(u)=g(u)+h(x),in R3,−Δϕ=2qF(u),in R3, $$ \textstyle\begin{cases} (a+\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}+b\int _{\mathbb{R}^{3}} u ^{2} )(-\Delta u+bu)+q\phi f(u)=g(u)+h(x), & \text{in } \mathbb{R}^{3}, \\ -\Delta \phi =2q F(u), & \text{in }\mathbb{R}^{3}, \end{cases} $$ where a>0 $a>0$, b≥0 $b\geq 0$ are constants, q≥0 $q\geq 0$ is a parameter, and F(t)=∫0tf(s)ds $F(t)=\int _{0}^{t}f(s)\,\mathrm{d}s$. Under some appropriate assumptions on g(u) $g(u)$ and h(x) $h(x)$, the existence of two positive radial solutions is proved by applying Ekeland’s variational principle and the mountain pass theorem. |
| first_indexed | 2024-12-11T02:14:21Z |
| format | Article |
| id | doaj.art-50980bd0c10c46fdba7eee431e150cdc |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-11T02:14:21Z |
| publishDate | 2019-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-50980bd0c10c46fdba7eee431e150cdc2022-12-22T01:24:12ZengSpringerOpenBoundary Value Problems1687-27702019-08-012019111610.1186/s13661-019-1252-7Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systemsHongxia Shi0School of Mathematics and Computational Science, Hunan First Normal UniversityAbstract This paper deals with the following generalized nonhomogeneous Kirchhoff–Schrödinger–Poisson system: {(a+∫R3|∇u|2+b∫R3u2)(−Δu+bu)+qϕf(u)=g(u)+h(x),in R3,−Δϕ=2qF(u),in R3, $$ \textstyle\begin{cases} (a+\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}+b\int _{\mathbb{R}^{3}} u ^{2} )(-\Delta u+bu)+q\phi f(u)=g(u)+h(x), & \text{in } \mathbb{R}^{3}, \\ -\Delta \phi =2q F(u), & \text{in }\mathbb{R}^{3}, \end{cases} $$ where a>0 $a>0$, b≥0 $b\geq 0$ are constants, q≥0 $q\geq 0$ is a parameter, and F(t)=∫0tf(s)ds $F(t)=\int _{0}^{t}f(s)\,\mathrm{d}s$. Under some appropriate assumptions on g(u) $g(u)$ and h(x) $h(x)$, the existence of two positive radial solutions is proved by applying Ekeland’s variational principle and the mountain pass theorem.http://link.springer.com/article/10.1186/s13661-019-1252-7Kirchhoff–Schrödinger–Poisson systemsVariational methodsCut-off functionalPohozaev type identity |
| spellingShingle | Hongxia Shi Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems Boundary Value Problems Kirchhoff–Schrödinger–Poisson systems Variational methods Cut-off functional Pohozaev type identity |
| title | Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems |
| title_full | Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems |
| title_fullStr | Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems |
| title_full_unstemmed | Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems |
| title_short | Positive solutions for a class of nonhomogeneous Kirchhoff–Schrödinger–Poisson systems |
| title_sort | positive solutions for a class of nonhomogeneous kirchhoff schrodinger poisson systems |
| topic | Kirchhoff–Schrödinger–Poisson systems Variational methods Cut-off functional Pohozaev type identity |
| url | http://link.springer.com/article/10.1186/s13661-019-1252-7 |
| work_keys_str_mv | AT hongxiashi positivesolutionsforaclassofnonhomogeneouskirchhoffschrodingerpoissonsystems |