关于一类半线性椭圆型方程存在无穷多解的注记

A Note on the Existence of Infinitely Many Solutions for a Class of Semilinear Elliptic Equations

本文考虑 n 维空间中有界光滑区域上的一类半线性椭圆型方程的边值问题.方程含有两项非线性项,第一项为奇函数具有次线性增长阶,第二项是超线性增长阶的非奇性扰动.证明了在适当的条件下无穷多个解的存在性.类似的问题已有过讨论,但这里直接考虑较一般的情形,并且所用的方法也与之不同.

In this paper,a class of semilinear elliptic type equations areconsidered on a bounded and smooth domain of n-dimension space.There are two nonlinear terms in the equations:one of them isa sublinear odd function,and the other a superlinear increase non-oddperturbation.It is proved that there exist infinitely many solutions forthe equations under some conditions.An extraordinary method is usedin the proof which is different from others;the conditions posed in thepaper are more general and reasonable.