| NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF INHOMOGENEOUS p-LAPLACE EQUATION |
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| 引用本文： | 戴求亿 彭丽辉. NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF NONNEGATIVE SOLUTIONS OF INHOMOGENEOUS p-LAPLACE EQUATION[J]. 数学物理学报(B辑英文版), 2007, 27(1): 34-56. DOI: 10.1016/S0252-9602(07)60004-6 |
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| 作者姓名： | 戴求亿 彭丽辉 |
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| 作者单位： | Department of Mathematics Hunan Normal University，Department of Mathematics Zhejiang University Changsha 410081，China，Hangzhou 310028，China |
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| 摘 要： | LetΩbe a smooth bounded domain in Rn. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation -△pu=|u|q-1u λf(x) onΩ, and identify necessary and sufficient conditions onΩand f(x) which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration.
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| 关 键 词： | 非齐次p-拉普拉斯方程 充要条件 非负解 狄利克雷问题 |
| 收稿时间： | 2004-10-09 |
| 修稿时间： | 2005-09-25 |
Necessary and sufficient conditions for the existence of nonnegative solutions of inhomogeneous p-Laplace equation |
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| Qiuyi Dai,Lihui Peng. Necessary and sufficient conditions for the existence of nonnegative solutions of inhomogeneous p-Laplace equation[J]. Acta Mathematica Scientia, 2007, 27(1): 34-56. DOI: 10.1016/S0252-9602(07)60004-6 |
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| Authors: | Qiuyi Dai Lihui Peng |
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| Affiliation: | aDepartment of Mathematics, Hunan Normal University, Changsha 410081, China;bDepartment of Mathematics, Zhejiang University, Hangzhou 310028, China |
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| Abstract: | Let Ω be a smooth bounded domain in Rn. In this article, we consider the homogeneous boundary Dirichlet problem of inhomogeneous p-Laplace equation -Δpu =|u|q-1u λf(x) on Ω, and identify necessary and sufficient conditions on Ω and f(x)which ensure the existence, or multiplicities of nonnegative solutions for the problem under consideration. |
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| Keywords: | Inhomogeneous p-Laplace equation Dirichlet problem nonnegative solution |
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