| 一类临界半线性双调和方程的多解存在性 |
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| 引用本文： | 曾宪忠,周俊. 一类临界半线性双调和方程的多解存在性[J]. 湖南科技大学学报(自然科学版), 2003, 18(2): 72-75 |
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| 作者姓名： | 曾宪忠 周俊 |
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| 作者单位： | 湖南科技大学,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(编号:10171029) |
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| 摘 要： | 给出了一类带非负扰动的临界半线性双调和方程的多解存在性。首先将方程化成一个椭圆方程组,然后根据椭圆方程组的正解的存在性获得了方程的第一个正解。最后,在不同的参数值和不同的维数条件下,用山路引理和一个改进的Pohozaev恒等式得到了方程的第二个正解的存在性和非存在性。参10。
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| 关 键 词： | 临界双调和方程 拟单调性 山路引理 多解存在性 |
| 文章编号： | 1000-9930(2003)02-0072-04 |
| 修稿时间： | 2002-10-29 |
Existence of multiple solutions for a Critical semilinear biharmonic equation |
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| ZENG Xian-zhong,ZHOU Jun. Existence of multiple solutions for a Critical semilinear biharmonic equation[J]. Journal of Hunan University of Science & Technology(Natural Science Editon), 2003, 18(2): 72-75 |
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| Authors: | ZENG Xian-zhong ZHOU Jun |
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| Abstract: | The existence of the multiple solutions of a critical semilinear biharmonic equation with a nonnegative perturbation has been studied. First, the equation is rewritten as a system of elliptic equations. Then, on the basis of the existence of the solution of the system of elliptic equations, the first positive solution of the equation is obtained. Finally, using the Pass Mountain Lemma and the improved Pohozaev's identity, the existence and the non-existence of the second positive solution of the equation are obtained respectively under different parameter value and different dimension conditions. 10refs. |
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| Keywords: | critical biharmonic equations quasi-monotonicity pass Mountain Lemma existence of multiple solutions |
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