方程—△u+f(|x|,u)=h(|x|)在环域上的边值问题的径向解的存在唯一性  

Existence and Uniquenes of Weakly Radial Solution for the Equation -△u+f(|x|, u)=h(|x|

作　　者：秦月君 

机构地区：[1]贵州大学数学系,贵阳550025

出　　处：《贵州大学学报（自然科学版）》1992年第3期129-134,共6页Journal of Guizhou University:Natural Sciences

摘　　要：本文研究当当n≥3时,半线性椭园型方程—△u+f(|x|,u)=h(|x|)在环域Ω={x∈R^n|0<r_1<|x|<r_2}上满足下列三种边值条件之一的边值问题(1),u|x|=r_1=u|x|=r_2=0;(2)|x|=r_1=u|x|=r_2=0;(3)u|x|=r_1=|x|=r_2=0 在f满足较少的条件下,利用单调算子理论证明了对于任意,h(t)∈L_2[r_1,r_2],上述三种边值问题都存在唯一的径向弱解u(r)∈L_2[r_1,r_2]。In this paper, we consider the boundary value problem of one of salisfying the following three bourdary value conditions for the semilinear elliptic equation-△u+j(|x|,u)=h(|x|) On the annulus Ω={x∈R^n|0<r_1<|x|<r_2} in the case n≥3. We prove that, these boundary value problems have the unique weakly radial salution for an arbitrary function h(t)∈L_2 [r_1, r_2], Using the theory of the monotone operator in the case that f satisfy a some of assumed conclitions.

关 键 词：半线性 椭园型方程 径向解 边值 

分 类 号：O175.25[理学—数学]