类p-Laplacian方程的特征值问题  

The Eigenvalue Problem for p-Laplacian-Like Equations

作　　者：陈祖墀[1] 罗涛[1] 

机构地区：[1]中国科学技术大学数学系,合肥230026

出　　处：《数学学报（中文版）》2003年第4期631-638,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10071080;10101024)

摘　　要：本文考虑类p-Laplacian方程-div(a(|Du|~p)|Du|^(p-2)Du)=λf(x,u),x∈Ω,u=0,x∈Ω的特征值问题,其中ΩR^n(n≥2)是有界光滑区域.当λ>0充分小,本质上仅在凸函数的假设下,得到了性质完全不同的两个特征函数的存在性,作为定理的应用,文中给出了两个实例.In this paper, we consider the eigenvalue problem for the p-Laplacian-like equation -div(a(|Du|p)|Du| p-2Du) = λf(x,u), χ∈Ω, u = 0,χ∈(?)Ω, where Ω(?) Rn (n ≥ 2) is a bounded smooth domain. Essentially the only under convexity assumption, when A > 0 small enough, we obtain the existence of two eigenfunctions which have very different asymptotic behaviors. As applications of our theorems, two examples in physics are given.

关 键 词：类p-Laplacian方程 山路引理 极六极小原理 

分 类 号：O175.6[理学—数学]