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凸区域上拟线性椭圆型方程的尖峰解

SPIKE-LAYERED SOLUTIONS OF A QUASILINEAR ELLIPTIC EQUATION ON CONVEX DOMAIN
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摘要 本文讨论奇异扰动的拟线性椭圆型方程-εΔ_pu(x)=f(u(x)),u(x)≥0,x∈Ω;u=0,x∈Ω在 Dirichlet边值条件下极小能量解的存在性和结构。其中ε>0是小参数,p>2,Δ_pu=div(|Du|^(p-2)Du),f(s)=s^q-s^(p-1),p-1<q<(Np)/(N-p)-1,Ω R^N(N≥2)是有界光滑区域。当ε→0时,方程存在一个极小能量解,应用移动平面方法可以证明此解在凸区域上会变成一个尖峰解。 In this paper the existence and structure of a least-energy solution are considered for a singularly perturbed quasilinear Dirichlet equation , where with is a small parameter and Ω is a bounded smooth domain in RN (N ≥2). The equation exists a least-energy solution as ε→ 0. Using the moving plane method it can be showed that this least-energy solution develops to a spike-layer solution when Ω is a convex domain.
作者 张正策 李开泰
机构地区 西安交通大学理学院
出处 《数学年刊（A辑）》 CSCD 北大核心 2003年第4期421-432,共12页 Chinese Annals of Mathematics
基金 国家重点学科基础研究基金(No.G1999032801) 国家自然学科基金(No.10001028)
关键词 拟线性椭圆型方程 尖峰解 移动平面方法 Quasilinear elliptic equation, Spike-layer solution, Moving plane method
分类号 O175.25 [理学—基础数学]
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参考文献28

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数学年刊（A辑）
2003年 第4期

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