Steady-state solutions for Schrodinger equations in photonic lattice
In this article, we study a nonlinear Schrodinger equation arising in optics. Firstly we prove the existence of multiple solutions of this equation. Secondly, we consider a nonlinear Schrodinger system which is intimately related to the Schrodinger equation. We obtain the existence of nontrivial...
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| Format: | Article |
| Language: | English |
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Texas State University
2018-05-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2018/109/abstr.html |
| _version_ | 1828882494317920256 |
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| author | Wen-Long Li |
| author_facet | Wen-Long Li |
| author_sort | Wen-Long Li |
| collection | DOAJ |
| description | In this article, we study a nonlinear Schrodinger equation arising in optics.
Firstly we prove the existence of multiple solutions of this equation.
Secondly, we consider a nonlinear Schrodinger system which is intimately
related to the Schrodinger equation. We obtain the existence of
nontrivial solutions to this system and we also get some results on
its positive solutions. Finally, assuming Dirichlet or Neumann boundary
condition, we show the existence and uniqueness of positive solution to
the Schrodinger equation. |
| first_indexed | 2024-12-13T10:30:39Z |
| format | Article |
| id | doaj.art-cd6d60b5be994ff787ad07c885ece34d |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-13T10:30:39Z |
| publishDate | 2018-05-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-cd6d60b5be994ff787ad07c885ece34d2022-12-21T23:50:53ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912018-05-012018109,112Steady-state solutions for Schrodinger equations in photonic latticeWen-Long Li0 Nanjing Univ., Nanjing 210093, China In this article, we study a nonlinear Schrodinger equation arising in optics. Firstly we prove the existence of multiple solutions of this equation. Secondly, we consider a nonlinear Schrodinger system which is intimately related to the Schrodinger equation. We obtain the existence of nontrivial solutions to this system and we also get some results on its positive solutions. Finally, assuming Dirichlet or Neumann boundary condition, we show the existence and uniqueness of positive solution to the Schrodinger equation.http://ejde.math.txstate.edu/Volumes/2018/109/abstr.htmlSchrodinger equationmultiple solutionspositive solutionnontrivial solution |
| spellingShingle | Wen-Long Li Steady-state solutions for Schrodinger equations in photonic lattice Electronic Journal of Differential Equations Schrodinger equation multiple solutions positive solution nontrivial solution |
| title | Steady-state solutions for Schrodinger equations in photonic lattice |
| title_full | Steady-state solutions for Schrodinger equations in photonic lattice |
| title_fullStr | Steady-state solutions for Schrodinger equations in photonic lattice |
| title_full_unstemmed | Steady-state solutions for Schrodinger equations in photonic lattice |
| title_short | Steady-state solutions for Schrodinger equations in photonic lattice |
| title_sort | steady state solutions for schrodinger equations in photonic lattice |
| topic | Schrodinger equation multiple solutions positive solution nontrivial solution |
| url | http://ejde.math.txstate.edu/Volumes/2018/109/abstr.html |
| work_keys_str_mv | AT wenlongli steadystatesolutionsforschrodingerequationsinphotoniclattice |