Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$
Abstract In this paper, we study the following Kirchhoff–Schrödinger–Poisson systems: {−(a+b∫R3|∇u|2dx)Δu+V(x)u+ϕu=f(u),x∈R3,−Δϕ=u2,x∈R3, $$\textstyle\begin{cases} -(a+b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\phi u=f(u), &x \in \mathbb{R}^{3}, \\ -\Delta \phi =u^{2},...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-04-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13661-019-1183-3 |
| _version_ | 1818311706692026368 |
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| author | Da-Bin Wang Tian-Jun Li Xinan Hao |
| author_facet | Da-Bin Wang Tian-Jun Li Xinan Hao |
| author_sort | Da-Bin Wang |
| collection | DOAJ |
| description | Abstract In this paper, we study the following Kirchhoff–Schrödinger–Poisson systems: {−(a+b∫R3|∇u|2dx)Δu+V(x)u+ϕu=f(u),x∈R3,−Δϕ=u2,x∈R3, $$\textstyle\begin{cases} -(a+b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\phi u=f(u), &x \in \mathbb{R}^{3}, \\ -\Delta \phi =u^{2}, &x\in \mathbb{R}^{3}, \end{cases} $$ where a, b are positive constants, V∈C(R3,R+) $V\in \mathcal{C}(\mathbb{R} ^{3},\mathbb{R}^{+})$. By using constraint variational method and the quantitative deformation lemma, we obtain a least-energy sign-changing (or nodal) solution ub $u_{b}$ to this problem, and study the energy property of ub $u_{b}$. Moreover, we investigate the asymptotic behavior of ub $u_{b}$ as the parameter b↘0 ${b\searrow 0}$. |
| first_indexed | 2024-12-13T08:06:13Z |
| format | Article |
| id | doaj.art-d89b6d1ba8dc41c28fbf41e30403197b |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-13T08:06:13Z |
| publishDate | 2019-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-d89b6d1ba8dc41c28fbf41e30403197b2022-12-21T23:54:19ZengSpringerOpenBoundary Value Problems1687-27702019-04-012019112010.1186/s13661-019-1183-3Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$Da-Bin Wang0Tian-Jun Li1Xinan Hao2Department of Applied Mathematics, Lanzhou University of TechnologyDepartment of Applied Mathematics, Lanzhou University of TechnologySchool of Mathematical Sciences, Qufu Normal UniversityAbstract In this paper, we study the following Kirchhoff–Schrödinger–Poisson systems: {−(a+b∫R3|∇u|2dx)Δu+V(x)u+ϕu=f(u),x∈R3,−Δϕ=u2,x∈R3, $$\textstyle\begin{cases} -(a+b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\phi u=f(u), &x \in \mathbb{R}^{3}, \\ -\Delta \phi =u^{2}, &x\in \mathbb{R}^{3}, \end{cases} $$ where a, b are positive constants, V∈C(R3,R+) $V\in \mathcal{C}(\mathbb{R} ^{3},\mathbb{R}^{+})$. By using constraint variational method and the quantitative deformation lemma, we obtain a least-energy sign-changing (or nodal) solution ub $u_{b}$ to this problem, and study the energy property of ub $u_{b}$. Moreover, we investigate the asymptotic behavior of ub $u_{b}$ as the parameter b↘0 ${b\searrow 0}$.http://link.springer.com/article/10.1186/s13661-019-1183-3Sign-changing solutionNonlocal termVariation methods |
| spellingShingle | Da-Bin Wang Tian-Jun Li Xinan Hao Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$ Boundary Value Problems Sign-changing solution Nonlocal term Variation methods |
| title | Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$ |
| title_full | Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$ |
| title_fullStr | Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$ |
| title_full_unstemmed | Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$ |
| title_short | Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$ |
| title_sort | least energy sign changing solutions for kirchhoff schrodinger poisson systems in r3 mathbb r 3 |
| topic | Sign-changing solution Nonlocal term Variation methods |
| url | http://link.springer.com/article/10.1186/s13661-019-1183-3 |
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