Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems
Abstract This paper is concerned with the existence of ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems in R3 $\mathbb {R}^{3}$ which have appeared in plasma physics, as well as in the description of high-power ultrashort lasers in matter. By employing a chan...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-04-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-018-0957-3 |
| _version_ | 1818284063350325248 |
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| author | Liejun Shen |
| author_facet | Liejun Shen |
| author_sort | Liejun Shen |
| collection | DOAJ |
| description | Abstract This paper is concerned with the existence of ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems in R3 $\mathbb {R}^{3}$ which have appeared in plasma physics, as well as in the description of high-power ultrashort lasers in matter. By employing a change of variables, the generalized quasilinear systems are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the mountain-pass geometric. Finally, we use Ekeland’s variational principle and the mountain-pass theorem to obtain the ground state solutions for the given problem. |
| first_indexed | 2024-12-13T00:46:51Z |
| format | Article |
| id | doaj.art-7d6fefaf6382460b9bc3fcd8f81c430b |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-13T00:46:51Z |
| publishDate | 2018-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-7d6fefaf6382460b9bc3fcd8f81c430b2022-12-22T00:05:01ZengSpringerOpenBoundary Value Problems1687-27702018-04-012018111710.1186/s13661-018-0957-3Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systemsLiejun Shen0Hubei Key Laboratory of Mathematical Sciences, Central China Normal UniversityAbstract This paper is concerned with the existence of ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems in R3 $\mathbb {R}^{3}$ which have appeared in plasma physics, as well as in the description of high-power ultrashort lasers in matter. By employing a change of variables, the generalized quasilinear systems are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the mountain-pass geometric. Finally, we use Ekeland’s variational principle and the mountain-pass theorem to obtain the ground state solutions for the given problem.http://link.springer.com/article/10.1186/s13661-018-0957-3Ground stateGeneralized quasilinearVariational principleMountain-pass theorem |
| spellingShingle | Liejun Shen Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems Boundary Value Problems Ground state Generalized quasilinear Variational principle Mountain-pass theorem |
| title | Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems |
| title_full | Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems |
| title_fullStr | Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems |
| title_full_unstemmed | Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems |
| title_short | Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems |
| title_sort | ground state solutions for a class of generalized quasilinear schrodinger poisson systems |
| topic | Ground state Generalized quasilinear Variational principle Mountain-pass theorem |
| url | http://link.springer.com/article/10.1186/s13661-018-0957-3 |
| work_keys_str_mv | AT liejunshen groundstatesolutionsforaclassofgeneralizedquasilinearschrodingerpoissonsystems |