含临界非线性项的p-双调和方程正解的存在性  

EXISTENCE RESULT OF POSITIVE SOLUTION FOR p-BIHARMONIC EQUATIONS INVOLVING CRITICAL GROWTH

作　　者：耿堤[1] 田继青[1] 邢小青[1] 

机构地区：[1]华南师范大学数学系,广东广州510631

出　　处：《华南师范大学学报（自然科学版）》2004年第4期23-28,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10371045);广东省自然科学基金资助项目(000671)

摘　　要：在n维空间中讨论了任一光滑有界区域上带有Navier边界条件的非线性p双调和方程,其中非线性项具有临界增长,证明了正解的存在性,将含临界增长的拉普拉斯方程的相应结果推广到了四阶方程的情形.In this paper a p-biharmonic equation involving critical growth with Navier boundary condition is considered on any bounded smooth domain in n-dimensions space. The existence of positive solution for the problem is obtained, which generalizes the corresponding result of Dirichlet problem for Laplacian equation involving critical growth to the case of fourth order equations.

关 键 词：正解的存在性 双调和方程 非线性项 临界增长 N维空间 四阶 有界区域 中非 边界条件 

分 类 号：O175[理学—数学] O241.82[理学—基础数学]