Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities
We consider the standing wave solutions for nonlinear fractional Schrödinger equations with focusing Hartree type and power type nonlinearities. We first establish the constrained minimization problem via applying variational method. Under certain conditions, we then show the existence of standing w...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/6837308 |
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| author | Na Zhang Jie Xin |
| author_facet | Na Zhang Jie Xin |
| author_sort | Na Zhang |
| collection | DOAJ |
| description | We consider the standing wave solutions for nonlinear fractional Schrödinger equations with focusing Hartree type and power type nonlinearities. We first establish the constrained minimization problem via applying variational method. Under certain conditions, we then show the existence of standing waves. Finally, we prove that the set of minimizers for the initial value problem of this minimization problem is stable. |
| format | Article |
| id | doaj-art-57696cd2d9874d7084c12d30bba398be |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-57696cd2d9874d7084c12d30bba398be2025-08-20T03:33:35ZengWileyAdvances in Mathematical Physics1687-91201687-91392016-01-01201610.1155/2016/68373086837308Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type NonlinearitiesNa Zhang0Jie Xin1School of Mathematics and Statistics Science, Ludong University, Yantai 264025, ChinaSchool of Mathematics and Statistics Science, Ludong University, Yantai 264025, ChinaWe consider the standing wave solutions for nonlinear fractional Schrödinger equations with focusing Hartree type and power type nonlinearities. We first establish the constrained minimization problem via applying variational method. Under certain conditions, we then show the existence of standing waves. Finally, we prove that the set of minimizers for the initial value problem of this minimization problem is stable.http://dx.doi.org/10.1155/2016/6837308 |
| spellingShingle | Na Zhang Jie Xin Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities Advances in Mathematical Physics |
| title | Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities |
| title_full | Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities |
| title_fullStr | Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities |
| title_full_unstemmed | Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities |
| title_short | Existence and Stability of Standing Waves for Nonlinear Fractional Schrödinger Equations with Hartree Type and Power Type Nonlinearities |
| title_sort | existence and stability of standing waves for nonlinear fractional schrodinger equations with hartree type and power type nonlinearities |
| url | http://dx.doi.org/10.1155/2016/6837308 |
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