The Existence of Positive Solution of a Nonlinear Problem on Unit Circle
We consider the following nonlinear problem u″x+λux+fx,u=0, x∈S1, (P) where S1 is a unit circle, λ∈ℝ is a parameter, and fx,u is a nonlinearity. By using the variational method, we obtain the existence of a positive solution to (P) for all λ∈ℝ. This phenomenon is different from the corresponding bou...
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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/10.1155/2020/5026268 |
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| _version_ | 1832550373799231488 |
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| author | Na Wei Yanli Zhou Xiangyu Ge |
| author_facet | Na Wei Yanli Zhou Xiangyu Ge |
| author_sort | Na Wei |
| collection | DOAJ |
| description | We consider the following nonlinear problem u″x+λux+fx,u=0, x∈S1, (P) where S1 is a unit circle, λ∈ℝ is a parameter, and fx,u is a nonlinearity. By using the variational method, we obtain the existence of a positive solution to (P) for all λ∈ℝ. This phenomenon is different from the corresponding boundary value problem. |
| format | Article |
| id | doaj-art-bdf10d7cb3ed44d4aa8d41d15f135f43 |
| 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-bdf10d7cb3ed44d4aa8d41d15f135f432025-02-03T06:06:55ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/50262685026268The Existence of Positive Solution of a Nonlinear Problem on Unit CircleNa Wei0Yanli Zhou1Xiangyu Ge2School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, ChinaSchool of Finance, Zhongnan University of Economics and Law, Wuhan 430073, ChinaDepartment of Finance, Wuhan Technology and Business University, Wuhan 430065, ChinaWe consider the following nonlinear problem u″x+λux+fx,u=0, x∈S1, (P) where S1 is a unit circle, λ∈ℝ is a parameter, and fx,u is a nonlinearity. By using the variational method, we obtain the existence of a positive solution to (P) for all λ∈ℝ. This phenomenon is different from the corresponding boundary value problem.http://dx.doi.org/10.1155/2020/5026268 |
| spellingShingle | Na Wei Yanli Zhou Xiangyu Ge The Existence of Positive Solution of a Nonlinear Problem on Unit Circle Journal of Function Spaces |
| title | The Existence of Positive Solution of a Nonlinear Problem on Unit Circle |
| title_full | The Existence of Positive Solution of a Nonlinear Problem on Unit Circle |
| title_fullStr | The Existence of Positive Solution of a Nonlinear Problem on Unit Circle |
| title_full_unstemmed | The Existence of Positive Solution of a Nonlinear Problem on Unit Circle |
| title_short | The Existence of Positive Solution of a Nonlinear Problem on Unit Circle |
| title_sort | existence of positive solution of a nonlinear problem on unit circle |
| url | http://dx.doi.org/10.1155/2020/5026268 |
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