| 临界非齐次多重调和方程的多解存在性 |
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| 引用本文： | 曾宪忠,黄力民,李爱翠.临界非齐次多重调和方程的多解存在性[J].湖南科技大学学报(自然科学版),2000,15(3):86-90. |
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| 作者姓名： | 曾宪忠 黄力民 李爱翠 |
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| 作者单位： | 湘潭工学院,数学与软件研究所,湖南,湘潭,411201 |
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| 基金项目： | 国家自然科学基金!资助项目 ( 1 961 0 34)，湖南省自然科学基金!资助项目 ( 99JJY2 0 0 3) |
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| 摘 要： | 讨论了带非负扰动的临界非齐次多重调和方程多解存在性和非存在性 .因为多重调和方程没有极值原理 ,所以首先利用泛函弱半连续性和适当变换辅助函数的方法建立起多重调和方程的上下解定理 由这个上下定理得到方程的第一个非负解 ,并讨论了第一个解的一些性质 再用山路引理和推广的Pohozave恒等式讨论了方程第二个解的存在性和非存在性 参 1 0 .
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| 关 键 词： | 多重调和方程 临界指数 弱半连续 上下解定理 多解存在性 |
| 修稿时间： | 1999-11-11 |
Existence of multiple solutions for a semilinear polyharmonic equation with critical exponent |
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| ZENG Xian-zhong,HUANG Li-min,LI Ai-cui.Existence of multiple solutions for a semilinear polyharmonic equation with critical exponent[J].Journal of Hunan University of Science & Technology(Natural Science Editon),2000,15(3):86-90. |
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| Authors: | ZENG Xian-zhong HUANG Li-min LI Ai-cui |
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| Abstract: | This paper deals with the existence and nonexistence of solutions for a critical semilinear polyharmonic equation with a non-negative perturbation. There isn't maximum principle for polyharmonic equation,so this paper first established a super-sub-sulution theorem via low semi-continuity and changed assistant function.Its first solution is obtained by the super-sub-solution theorem and some interesting results of the first solution are discussed. The existence and nonexistence of its second solution are proved by empolying mountain pass lemma and by using improving well-known Pohozaev's identity in a certain condition.10refs. |
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| Keywords: | polyharmonic equation critical exponent lower semi-continuity super-sub-solution existence of multiple solutions |
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