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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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 |
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doaj-7d6fefaf6382460b9bc3fcd8f81c430b2020-11-24T23:56:10ZengSpringerOpenBoundary 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Liejun Shen |
| 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 |
| author_facet |
Liejun Shen |
| author_sort |
Liejun Shen |
| title |
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_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_sort |
ground state solutions for a class of generalized quasilinear schrödinger–poisson systems |
| publisher |
SpringerOpen |
| series |
Boundary Value Problems |
| issn |
1687-2770 |
| publishDate |
2018-04-01 |
| 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. |
| 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 |
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1725459303597342720 |