一个临界带权椭圆问题解的Morse指标

Morse index of solutions for a critical weighted elliptic problem

本文研究下面临界带权的椭圆问题:-div(|x|~θ?u)=(N′+τ)(N′-2)|x|~?u^(pτ),在RN中,u>0,在RN其中,N′=N+θ>2,τ=?-θ>-2,p_τ=(N′+2+2τ)/(N′-2).杜一宏和郭宗明(2015)证明了上述问题有一族有限Morse指标解.本文的主要目的是给出这些解Morse指标的精确刻画,从而得到这族解的Morse指标仅依赖于N、τ和θ.中,

In this paper, we study the following critical weighted elliptic problem： {-div（｜x｜^θ u）=（N′＋τ）（N′-2）｜x｜^ιuPτ,inR^N,u〉0,inR^N Du and Guo （2015） showed the above problem possesses where N′=N＋θ〉2,τ=ι-θ〉-2,Pτ=N′＋2＋2τ/N′-2 a family of finite Morse index solutions. Our main aim in this paper is to give its exact characterization of Morse index, which depends only on N, τ- and θ.