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R^2中含临界位势的非线性椭圆问题 被引量:4

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摘要 考虑R2中的含临界位势的非线性椭圆方程齐次Dirichlet问题.通过建立一常数为最佳的含权不等式,确定了临界位势,并讨论了含临界位势的Laplace方程特征值问题.通过建立含一个奇点的解的Pohozaev型恒等式并结合Cauchy-Kovalevskaya定理得到了含临界位势非线性椭圆型方程有奇点的解的不存在性结果.此外,利用山路定理和特征值的性质得到了这一问题多重解的存在性的一系列结果.
出处 《中国科学(A辑)》 CSCD 北大核心 2004年第5期610-624,共15页 Science in China(Series A)
基金 国家自然科学基金(批准号:lOl71032) 广东省自然科学基金资助项目
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同被引文献29

  • 1陈志辉,沈尧天,姚仰新.R^4中含位势的非线性双调和方程[J].数学年刊(A辑),2005,26(4):487-494. 被引量:7
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  • 3何跃.一类退化椭圆型方程Dirichlet问题的解的高阶正则性[J].南京师大学报(自然科学版),2007,30(1):28-32. 被引量:1
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