一类拟线性椭圆方程径向整体正解的分类性质 献给余家荣教授100华诞

Classification of positive radial entire solutions for some quasilinear elliptic equations

本文对如下拟线性方程整体径向正解进行分类研究:{r^-γ(rα|u′|βu′)′+|u|p-1u=0, 0<r<∞ u(0)=ρ>0, u′(0)=0.这类方程中的微分算子包含了径向函数空间中通常的Laplace算子、m-Laplace算子和k-Hessian算子.本文研究该类方程的任意两个解(包括奇异解)之间的相交和分离的性质,完整地给出各种情形下它们之间的相交数,解决了Miyamoto (2016)未解的一种情形.

We classify positive radial entire solutions of the quasilinear elliptic equation{r^-γ(rα|u′|βu′)′+|u|p-1u=0, 0<r<∞ u(0)=ρ>0, u′(0)=0.The differential operator in the equation includes the usual Laplace, m-Laplace, and k-Hessian operators in the space of radial functions. We study the intersection properties and the separation properties of two arbitrary solutions(including the singular solution). We present a complete classification picture of the intersection number and solve a left case by Miyamoto(2016).