Ground states for Schrodinger-Poisson systems with three growth terms
In this article we study the existence and nonexistence of ground states of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3, }$$ where V, K, and Q are asymptotically periodic in the va...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2014-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2014/253/abstr.html |
| _version_ | 1818511892136591360 |
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| author | Hui Zhang Fubao Zhang Junxiang Xu |
| author_facet | Hui Zhang Fubao Zhang Junxiang Xu |
| author_sort | Hui Zhang |
| collection | DOAJ |
| description | In this article we study the existence and nonexistence
of ground states of the Schrodinger-Poisson system
$$\displaylines{
-\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr
-\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3,
}$$
where V, K, and Q are asymptotically periodic in the variable x.
The proof is based on the the method of Nehari manifold and concentration
compactness principle. In particular, we develop the method of Nehari manifold
for Schrodinger-Poisson systems with three times growth. |
| first_indexed | 2024-12-10T23:39:13Z |
| format | Article |
| id | doaj.art-675614a1d04f42ee9cdd24377d2cbe89 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-10T23:39:13Z |
| publishDate | 2014-12-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-675614a1d04f42ee9cdd24377d2cbe892022-12-22T01:29:06ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-12-012014253,113Ground states for Schrodinger-Poisson systems with three growth termsHui Zhang0Fubao Zhang1Junxiang Xu2 Jinling Institute of Technology, Nanjing, China Southeast Univ., Nanjing, China Southeast Univ., Nanjing, China In this article we study the existence and nonexistence of ground states of the Schrodinger-Poisson system $$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\Delta\phi=K(x)u^2, \quad x\in \mathbb{R}^3, }$$ where V, K, and Q are asymptotically periodic in the variable x. The proof is based on the the method of Nehari manifold and concentration compactness principle. In particular, we develop the method of Nehari manifold for Schrodinger-Poisson systems with three times growth.http://ejde.math.txstate.edu/Volumes/2014/253/abstr.htmlSchrodinger-Poisson systemvariational methodground stateasymptotically periodic |
| spellingShingle | Hui Zhang Fubao Zhang Junxiang Xu Ground states for Schrodinger-Poisson systems with three growth terms Electronic Journal of Differential Equations Schrodinger-Poisson system variational method ground state asymptotically periodic |
| title | Ground states for Schrodinger-Poisson systems with three growth terms |
| title_full | Ground states for Schrodinger-Poisson systems with three growth terms |
| title_fullStr | Ground states for Schrodinger-Poisson systems with three growth terms |
| title_full_unstemmed | Ground states for Schrodinger-Poisson systems with three growth terms |
| title_short | Ground states for Schrodinger-Poisson systems with three growth terms |
| title_sort | ground states for schrodinger poisson systems with three growth terms |
| topic | Schrodinger-Poisson system variational method ground state asymptotically periodic |
| url | http://ejde.math.txstate.edu/Volumes/2014/253/abstr.html |
| work_keys_str_mv | AT huizhang groundstatesforschrodingerpoissonsystemswiththreegrowthterms AT fubaozhang groundstatesforschrodingerpoissonsystemswiththreegrowthterms AT junxiangxu groundstatesforschrodingerpoissonsystemswiththreegrowthterms |