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

作　　者：安荣[1,2] 张正策[2] 李媛[2] 李开泰[2] 

机构地区：[1]温州大学数学与信息科学学院,浙江温州325035 [2]西安交通大学理学院,西安710049

出　　处：《数学年刊（A辑）》2009年第1期85-96,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10571142;No.10701061)资助的项目.

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.In this paper, a class of fourth-order degenerate elliptic problem involving pbiharmonic 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.

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 

分 类 号：O175.29[理学—数学]