半线性双调和方程奇异位势问题的非平凡解  

Nontrivial Solutions to Semilinear Biharmonic Equation with Singular Critical Potential

作　　者：熊辉[1] 陈祖墀[1] 

机构地区：[1]中国科学技术大学数学系

出　　处：《中国科学技术大学学报》2005年第6期777-782,共6页JUSTC

基　　金：国家自然科学基金资助项目(10371116).

摘　　要：研究了在四维空间R4中球域B内的半线性奇异双调和方程的Dirichlet边值问题.其中,奇异项中不但含有通常的奇位势,还含有对数权,使得该奇异项成为R4空间中的临界位势.文中首先建立了相应的Hardy不等式,然后通过山路引理得出了该问题非平凡解的存在性.A semilinear singular biharmonic equation with Dirichlet boundary condition is investigated in the ball B belong to R^4 . Not only is the common singular potential is contained in the singular item, but the logarithm weighted is involved so that the singular item becomes the critical potential in R^4. The relative Hardy inequality is established first, and then by Mountain Pass theorem the existence of nontrivial solutions is obtained.

关 键 词：HARDY不等式 临界奇异位势 对数权 

分 类 号：O175.6[理学—数学]