一类带奇异项的半线性椭圆型方程的不变解

Invariational Solutions of a Singular Elliptic Equation

主要研究一类带奇异项的半线性椭圆型方程在,Ω=Ω1×Rd条件下的不变解的存在情况。若Sλμ,(Ω,G)<S0μ(Ω,G),则Sλμ(Ω,G),可以达到,根据这个思路来证明解的存在性。当d≥2时,方程(1)至少有一个不变解;当d=1且λ足够小的条件下,方程(1)至少有一个不变解。

This paper is devoted to the existence of invariant solutions of a singular elliptic under Ω=Ω1×R^d We have proved the existence of these solutions using the idea of proving that Sλ^μ（Ω,G）is achieved if Sλ^μ（Ω,G）〈So^μ（Ω,G）When d≥2there is at least one invariant solution of Equation （1）; When d= 1, the situation is quite different, and we can assure the existence of solution only if λ is small enough.