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

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.