| 退化非线性椭圆方程Dirichlet问题解的存在性 |
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| 引用本文： | 姚爷新.退化非线性椭圆方程Dirichlet问题解的存在性[J].华南理工大学学报(自然科学版),1992,20(3):98-103. |
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| 作者姓名： | 姚爷新 |
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| 作者单位： | 华南理工大学应用数学系 |
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| 摘 要： | 本文利用山路引理在加权的索伯列夫空间讨论一类退化非线性椭圆方程Dirichlet问题的非平凡解的存在性;我们还利用Pohozeav恒等式证明在一定条件下该方程不存在非平凡解。
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| 关 键 词： | 椭圆型方程 非线性 Dirichlet |
THE EXISTENCE OF SOLUTIONS OF THE DIRICHLET PROBLEM FOR A DEGENERATE NONLINEAR ELLIPTIC EQUATION |
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| Yao Yangxin.THE EXISTENCE OF SOLUTIONS OF THE DIRICHLET PROBLEM FOR A DEGENERATE NONLINEAR ELLIPTIC EQUATION[J].Journal of South China University of Technology(Natural Science Edition),1992,20(3):98-103. |
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| Authors: | Yao Yangxin |
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| Abstract: | In this paper we discuss the existence of nontrivial solutions of the Dirichlet problem for a degenerate nonlinear elliptic equation in the weighted sobolev space by virtue of the Mountain Pass Lemma. We have also proved that the equation has no nontrivial solution in some conditions by means of a Pohozeav-type identity. |
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| Keywords: | elliptic equations weighted Sobolev space non-linear/mountain pass lemma Palais-Smale condition relative compactness |
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