Nonlinear Biharmonic Equations with Critical Potential  被引量:6

Nonlinear Biharmonic Equations with Critical Potential

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作  者:Hui XIONG Yao Tian SHEN 

机构地区:[1]Department of Applied Mathematics, South China University of Technology, Guangzhou 510640, P. R. China [2]Department of Mathematics,University of Technology of Dongguan, Donguan 523106, P, R. China

出  处:《Acta Mathematica Sinica,English Series》2005年第6期1285-1294,共10页数学学报(英文版)

基  金:the National Natural Science Foundation of China (Nos.10171032,10071080,10101024)

摘  要:In this paper, we study two semilinear singular biharmonic equations: one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile, we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result.In this paper, we study two semilinear singular biharmonic equations: one with subcritical exponent and critical potential, another with sub-critical potential and critical exponent. By Pohozaev identity for singular solution, we prove there is no nontrivial solution for equations with critical exponent and critical potential. And by using the concentrate compactness principle and Mountain Pass theorem, respectively, we get two existence results for the two problems. Meanwhile, we have compared the changes of the critical dimensions in singular and non-singular cases, and we get an interesting result.

关 键 词:Critical potential SINGULARITY Critical dimensions Disappear 

分 类 号:O175[理学—数学]

 

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