Acta mathematica scientia,Series A ›› 2003, Vol. 23 ›› Issue (1): 106-114.

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SobolevHardy Inequalities and Some Critical Biharmonic Problems

 KANG Dong-Sheng, DENG Yin-Bin   

  • Online:2003-02-25 Published:2003-02-25
  • Supported by:

    国家自然科学基金资助项目

Abstract:

This paper considers the biharmonic equation with singular coefficient〖JB({〗△2u-μ[SX(]u[]|x|s[SX)]=f(x,u),\=
u=[SX(]u[]ν[SX)]=0,〖JB)〗\ \ 〖JB(〗x∈Ω,x∈Ω,[JB)where ΩR\+N is a smooth bounded domain, μ∈R is a parameter,
0≤s≤2,N≥5,u∈H\+2\-0(Ω),△\+2=△△ denotes iterated Ndimensional Laplacian. When f(x,u)=u\+p,p=[SX(]2N[]N-4[SX)], the above problem becomes a critical biharmonic problem.Some results about the existence of its solutions are obtained by SobolevHardy inequalities and variational methods.

Key words: SobolevHardy inequaliy; Biharmonic equation; Variational method; Existenceof solution

CLC Number: 

  • 35J30
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