具临界指数及奇异性的双调和方程解的存在性

Abstract

Abstract:

In this paper, the authors present a result on existence to the following singular biharmonic equation involving
singular terms
{?²u-μ/|x|^αμ = λg(x)μ+k(x)|μ|^q-2 μ+|μ|^2*-2 μ, x ∈ Ω,
μ ∈D₀^2,2(Ω), x ∈∂Ω,

where Ω is a bounded domain containing origin, Ω ( R^N, N ≥ 5, 0 ≤ α, s < 4,2 < q < 2^*(s) = 2(N-s)/N-4}, and g(x), k(x) are nonnegative functions, the existence of solution is shown by variational method, the acquired function for the imbedding mapping D^2,2(R^N) → L²*(R^N) plays an important role in the discussion.

Key words: Critical exponent, Variational method, Singular

CLC Number:

35J25

Cite this article

PENG Yan-Fang, ZHANG Zheng-Jie. Existence of Solution for a |Singular Biharmonic Equation Involving Critical Exponent[J].Acta mathematica scientia,Series A, 2009, 29(6): 1492-1499.

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References

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Existence of Solution for a |Singular Biharmonic Equation Involving Critical Exponent

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