Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth
In this paper, we prove the multiplicity of nontrivial solutions for a class of fractional-order elliptic equation with magnetic field. Under appropriate assumptions, firstly, we prove that the system has at least two different solutions by applying the mountain pass theorem and Ekeland’s variationa...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/7817843 |
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| _version_ | 1832556882082922496 |
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| author | Jianwen Zhou Bianxiang Zhou Yanning Wang |
| author_facet | Jianwen Zhou Bianxiang Zhou Yanning Wang |
| author_sort | Jianwen Zhou |
| collection | DOAJ |
| description | In this paper, we prove the multiplicity of nontrivial solutions for a class of fractional-order elliptic equation with magnetic field. Under appropriate assumptions, firstly, we prove that the system has at least two different solutions by applying the mountain pass theorem and Ekeland’s variational principle. Secondly, we prove that these two solutions converge to the two solutions of the limit problem. Finally, we prove the existence of infinitely many solutions for the system and its limit problems, respectively. |
| format | Article |
| id | doaj-art-466e5a7626b748b6b95522ccb087a357 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-466e5a7626b748b6b95522ccb087a3572025-02-03T05:44:12ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/78178437817843Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable GrowthJianwen Zhou0Bianxiang Zhou1Yanning Wang2Department of Mathematics, Yunnan University, Kunming, Yunnan 650091, ChinaDepartment of Mathematics, Yunnan University, Kunming, Yunnan 650091, ChinaSchool of Basic Medical Science, Kunming Medical University, Kunming, Yunnan 650500, ChinaIn this paper, we prove the multiplicity of nontrivial solutions for a class of fractional-order elliptic equation with magnetic field. Under appropriate assumptions, firstly, we prove that the system has at least two different solutions by applying the mountain pass theorem and Ekeland’s variational principle. Secondly, we prove that these two solutions converge to the two solutions of the limit problem. Finally, we prove the existence of infinitely many solutions for the system and its limit problems, respectively.http://dx.doi.org/10.1155/2020/7817843 |
| spellingShingle | Jianwen Zhou Bianxiang Zhou Yanning Wang Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth Journal of Function Spaces |
| title | Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth |
| title_full | Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth |
| title_fullStr | Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth |
| title_full_unstemmed | Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth |
| title_short | Multiplicity Results for Variable-Order Nonlinear Fractional Magnetic Schrödinger Equation with Variable Growth |
| title_sort | multiplicity results for variable order nonlinear fractional magnetic schrodinger equation with variable growth |
| url | http://dx.doi.org/10.1155/2020/7817843 |
| work_keys_str_mv | AT jianwenzhou multiplicityresultsforvariableordernonlinearfractionalmagneticschrodingerequationwithvariablegrowth AT bianxiangzhou multiplicityresultsforvariableordernonlinearfractionalmagneticschrodingerequationwithvariablegrowth AT yanningwang multiplicityresultsforvariableordernonlinearfractionalmagneticschrodingerequationwithvariablegrowth |