| 安荣,张正策,李媛,李开泰.具有指数增长的非线性p-双调和问题解的存在性和非存在性[J].数学年刊A辑,2009,30(1):85~96 |
| 具有指数增长的非线性p-双调和问题解的存在性和非存在性 |
| Existence and Nonexistence of Solutions of Nonlinear p-Biharmonic Problem with Exponential Growth |
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| DOI： |
| 中文关键词: P双调和问题 指数增长 存在性和非存在性 变分方法 |
| 英文关键词:p-biharmonic problem, Exponential growth, Existence and
nonexistence, Variational method |
| 基金项目:国家自然科学基金 |
| Author Name | Affiliation | E-mail | | AN Rong | College of Mathematics and Information Science, Wenzhou University,
Wenzhou 325035, Zhejiang, China. | anrong702@hotmail.com | | ZHANG Zhengce | School of Science, Xi’an Jiaotong University, Xi’an 710049, China. | | | LI Yuan | School of Science, Xi’an Jiaotong University, Xi’an 710049, China. | | | LI Kaitai | School of Science, Xi’an Jiaotong University, Xi’an 710049, China. | |
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| 中文摘要: |
| 主要考虑了具有指数增长的4阶退化P-双调和问题弱解的存在性和非存在性.当n≥2p+1和2p≥n时,这些结果是不同的.尽管对高阶问题,弱比较原理不再成立,但是仍有其他一些方法可以使用.当2p≥n时,采用的是极小极大方法,而当n≥2p+1时,采用的是上下解方法.最后给出了当n≥2p+1时正则解的渐近行为. |
| 英文摘要: |
| In this paper, a class of fourth-order degenerate elliptic problem involving p-
biharmonic operator with exponential growth is investigated in a smooth domain. The
existence and nonexistence of solutions in the weak sense are studied. But some results
are different between n > 2p + 1 and 2p > n. Although weak comparison principle is not
available for high-order problem, other methods still are available. Here, the authors use
the minimax method if 2p > n and the method of upper and lower solutions if n > 2p + 1.
Finally, the asymptotic behavior of regular solution is established if n > 2p + 1. |
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