一类含Hardy位势的双调和方程解的存在性  

Existence of Solutions to a Class of Biharmonic Equation with Hardy Potential

作　　者：王友军[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）》2008年第12期142-145,共4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(10471047);广东自然科学基金资助项目(05300159)

摘　　要：构造了一个新的Sobolev空间,建立了紧嵌入定理,分析了含临界参数双调和方程的特征值问题,最后根据含有Cerami条件的山路引理,在这个新空间中讨论了一类含Hardy位势及临界参数的双调和方程非平凡解的存在性.In this paper, a new Sobolev space is established and a compact embedding theorem is given. Then, the eigenvalue problem of the biharmonic equation with critical exponents is analyzed. Finally, by using the Mountain Pass Lemma satisfying the Cerami condition, the existence of the nontrivial solutions to a class of biharmonic equation with Hardy potential and critical parameter is discussed in the established Sobolev space.

关 键 词：双调和方程 HARDY位势 临界指数 存在性 CERAMI条件 

分 类 号：O175.10[理学—数学]