| EXISTENCE,MULTIPLICITY AND STABILITY RESULTS FOR POSITIVE SOLUTIONS OF NONLINEAR p-LAPLACIAN EQUATIONS |
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| 作者姓名： | MA Li SU Ning |
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| 作者单位： | MA Li
SU NING Department of Mathematical Sciences，Tsinghua University，Beijing 100084，China. Department of Mathematical Sciences，Tsinghua University，Beijing 100084，China. |
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| 基金项目： | Project supported by the 973 Project of the Ministry of Science and Technology of China (No.G1999075107)，a Scientific Grant of Tsinghua University. |
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| 摘 要： | This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator:-△pu=λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of the Crandall-Rabinowitz bifurcation theory to this problem. Typical examples are checked in detail and multiplicity of the solutions are illustrated. Then the stability for the associated parabolic equation is considered and a Fujita-type result is presented.
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| 关 键 词： | 多样性 稳定性 正解 非线性 拉普拉斯算子 |
| 收稿时间： | 7/2/2024 12:00:00 AM |
| 修稿时间： | 1/3/2007 12:00:00 AM |
EXISTENCE, MULTIPLICITY AND STABILITY RESULTS FOR POSITIVE SOLUTIONS OF NONLINEAR p-LAPLACIAN EQUATIONS |
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| MA Li,SU Ning.EXISTENCE,MULTIPLICITY AND STABILITY RESULTS FOR POSITIVE SOLUTIONS OF NONLINEAR p-LAPLACIAN EQUATIONS[J].Chinese Annals of Mathematics,Series B,2004,25(2):275-286. |
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| Authors: | MA Li and SU Ning |
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| Institution: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.
2. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China |
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| Abstract: | This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator: -△pu = λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of the Crandall-Rabinowitz bifurcation theory to this problem. Typical examples are checked in detail and multiplicity of the solutions are illustrated. Then the stability for the associated parabolic equation is considered and a Fujita-type result is presented. |
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| Keywords: | p-Laplacian operator Bifurcation Multiplicity Positive solutions |
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