一带权多重调和方程正解的存在性及渐近行为

Abstract

Abstract:

In this paper, the author establishes a prior estimate of the radially symmetric solutions, and apply a Poho{z}aev-type identity to the research on the existence of solutions for the polyharmonic equation
{(-Δ)^mu=|x|^αu^p-1, u>0, in B,
Dⁱu|_∂B=0, |i|≤m-1
where m ∈N, B is the unit ball in Rⁿ with n≥2m+1, α>0 and p>2. Moreover, by making use of the Blow-up analysis, the asymptotic behaviour of the least energy solutions for above equation is obtained when α is fixed and p→2n/(n-2m) .

Key words: Polyhamonic equation, Critical Sobolev exponent, Radially symmetric solution, Asymptotic behaviour, Symmetry breaking

CLC Number:

35B40

WANG Zhong-Liang. Existence and Asymptotic Behaviour of Positive Solutions for a Polyharmonic Equation with Weight[J].Acta mathematica scientia,Series A, 2013, 33(5): 829-841.

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Existence and Asymptotic Behaviour of Positive Solutions for a Polyharmonic Equation with Weight

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