| Existence and uniqueness of positive solutions of semilinear elliptic equations |
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| 作者姓名： | Qiu-yi DAI~ |
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| 作者单位： | Qiu-yi DAI（Department of Mathematics, Hunan Normal University, Changsha 410081, China） ;
Yu-xia FU（Department of Applied Mathematics, Hunan University, Changsha 410082, China） ;
Yong-geng GU（Department of Mathematics, Hunan Normal University, Changsha 410081, China） ; |
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| 摘 要： | This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained.
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Existence and uniqueness of positive solutions of semilinear elliptic equations |
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| Qiu-yi DAI.Existence and uniqueness of positive solutions of semilinear elliptic equations[J].Science in China(Mathematics),2007,50(8):1141-1156. |
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| Authors: | Qiu-yi Dai Yu-xia Fu Yong-geng Gu |
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| Institution: | 1. Department of Mathematics, Hunan Normal University, Changsha 410081, China
2. Department of Applied Mathematics, Hunan University, Changsha 410082, China |
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| Abstract: | This paper is devoted to the study of existence,uniqueness and non-degeneracy of positive solutions of semi-linear elliptic equations.A necessary and sufficient condition for the existence of positive solutions to problems is given.We prove that if the uniqueness and non-degeneracy results are valid for positive solutions of a class of semi-linear elliptic equations,then they are still valid when one perturbs the differential operator a little bit.As consequences,some uniqueness results of positive solutions under the domain perturbation are also obtained. |
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| Keywords: | semilinear elliptic equation positive solution existence uniqueness nondegeneracy |
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