有界洞型区域上一类半线性椭圆型方程的可解性  

Solvability for Certain Semi-linear Elliptic Equations in the Bounded Domain with a Hole

作　　者：朱君珏[1] 张正青[1] 钟金标[1] 

机构地区：[1]安庆师范学院数学与计算科学学院,安徽安庆246133

出　　处：《安庆师范学院学报（自然科学版）》2013年第2期1-3,31,共4页Journal of Anqing Teachers College(Natural Science Edition)

摘　　要：利用上、下解方法,嵌入定理及Leray—Schauder不动点理论证明了一类半线性椭圆型方程在洞型区域内边值问题弱解的存在。利用Schauder不动点理论及上、下解方法证明了经典解的存在。In this paper, the existence of the weak solutions to a class of semi - linear elliptic equations in the Bounded do- main with a hole is proved. The main tools to prove our theorems are the sub - super solution method and imbeded theorem and Le- ray - Schauder fixed Point theorem also, we proved the existence of the classical solutions by using of the Sub - super solution method and Schauder fixed point theorem.

关 键 词：上、下解 Leray-Schauder不动点理论 嵌入定理 

分 类 号：O175.2[理学—数学]