Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems
We consider the following double phase problem with variable exponents: −div∇upx−2∇u+ax∇uqx−2∇u=λfx,u in Ω,u=0, on ∂Ω. By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some assumptions. Moreover, infinitely many pairs of solution...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/8237492 |
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| author | Jie Yang Haibo Chen Senli Liu |
| author_facet | Jie Yang Haibo Chen Senli Liu |
| author_sort | Jie Yang |
| collection | DOAJ |
| description | We consider the following double phase problem with variable exponents: −div∇upx−2∇u+ax∇uqx−2∇u=λfx,u in Ω,u=0, on ∂Ω. By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some assumptions. Moreover, infinitely many pairs of solutions are provided by applying the Fountain Theorem, Dual Fountain Theorem, and Krasnoselskii’s genus theory. |
| format | Article |
| id | doaj-art-3b1f0f5d60014292b7ac351820cf2efb |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-3b1f0f5d60014292b7ac351820cf2efb2025-02-03T01:05:12ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/82374928237492Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase ProblemsJie Yang0Haibo Chen1Senli Liu2School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, ChinaSchool of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, ChinaWe consider the following double phase problem with variable exponents: −div∇upx−2∇u+ax∇uqx−2∇u=λfx,u in Ω,u=0, on ∂Ω. By using the mountain pass theorem, we get the existence results of weak solutions for the aforementioned problem under some assumptions. Moreover, infinitely many pairs of solutions are provided by applying the Fountain Theorem, Dual Fountain Theorem, and Krasnoselskii’s genus theory.http://dx.doi.org/10.1155/2020/8237492 |
| spellingShingle | Jie Yang Haibo Chen Senli Liu Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems Advances in Mathematical Physics |
| title | Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems |
| title_full | Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems |
| title_fullStr | Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems |
| title_full_unstemmed | Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems |
| title_short | Existence and Multiplicity of Solutions for a Class of Anisotropic Double Phase Problems |
| title_sort | existence and multiplicity of solutions for a class of anisotropic double phase problems |
| url | http://dx.doi.org/10.1155/2020/8237492 |
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