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

作　　者：张正策[1] 李开泰[1] 

机构地区：[1]西安交通大学理学院,西安710049

出　　处：《数学年刊（A辑）》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)

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.

关 键 词：拟线性椭圆型方程 尖峰解 移动平面方法 

分 类 号：O175.25[理学—数学]