| On a nonlinear elliptic problem with critical potential in R~2 |
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| 作者姓名： | SHEN Yaotian YAO Yangxin & CHEN Zhihui |
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| 作者单位： | SHEN Yaotian，YAO Yangxin & CHEN Zhihui
Department of Applied Mathematics，South China University of Technology，Guangzhou 510640，China |
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| 基金项目： | 国家自然科学基金，国家自然科学基金 |
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| 摘 要： | Consider the existence of nontrivial solutions of homogeneous Dirichlet problem for a nonlinear elliptic equation with the critical potential in R2. By establishing a weighted inequality with the best constant, determine the critical potential in R2, and study the eigenvalues of Laplace equation with the critical potential. By the Pohozaev identity of a solution with a singular point and the Cauchy-Kovalevskaya theorem, obtain the nonexis tence result of solutions with singular points to the nonlinear elliptic equation. Moreover, for the same problem, the existence results of multiple solutions are proved by the mountain pass theorem.
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On a nonlinear elliptic problem with critical potential in R2 |
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| SHEN Yaotian,YAO Yangxin & CHEN Zhihui.On a nonlinear elliptic problem with critical potential in R~2[J].Science in China(Mathematics),2004,47(5). |
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| Authors: | SHEN Yaotian Yao Yangxin HEN Zhihui |
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| Institution: | Department of Applied Mathematics, South China University of Technology, Guangzhou 510640, China |
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| Abstract: | Consider the existence of nontrivial solutions of homogeneous Dirichlet problem for a nonlinear elliptic equation with the critical potential in R2. By establishing a weighted inequality with the best constant, determine the critical potential in R2, and study the eigenvalues of Laplace equation with the critical potential. By the Pohozaev identity of a solution with a singular point and the Cauchy-Kovalevskaya theorem, obtain the nonexis tence result of solutions with singular points to the nonlinear elliptic equation. Moreover, for the same problem, the existence results of multiple solutions are proved by the mountain pass theorem. |
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| Keywords: | elliptic equation Hardy inequality critical potential mountain pass theorem |
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