含临界位势和不定权的非线性双调和问题  

Nonlinear Biharmonic Problem with Critical Potential and Indefinite Potential

作　　者：张贻民[1] 沈尧天[1] 

机构地区：[1]华南理工大学数学系,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2009年第7期142-146,共5页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10771074)

摘　　要：考虑了R4中一类含临界位势和不定权的非线性双调和问题,在次临界增长的条件下,证明了临界位势中的最佳指数,并利用一个最佳的Hardy不等式和第一特征值的性质,证明了非平凡解的存在性.This paper deals with a class of nonlinear biharmonic problem with critical potential and indefinite potential in R4. In the investigation, the exponent in critical potential is proved optimal, and the existence of the nontrivial solution is proved by using an optimal Hardy inequality and the character of the first eigenvalue.

关 键 词：次临界增长 HARDY不等式 临界位势 

分 类 号：O175.25[理学—数学]