具临界指数p-Laplace方程在R^N上的结点径向解

NODAL RADIAL SOLUTIONS OF THE QUASILINEAR p-Laplace EQUATION INVOLVING CRITICAL SOBOLEV EXPONENT IN R^N

研究了具临界Ｓｏｂｏｌｅｖ 指数拟线性椭圆型方程－ ｄｉｖ（｜ｕ｜ｐ－ ２ｕ） ＝ Ｋ（｜ｘ｜）｜ｕ｜ｐ－ ２ｕ，ｘ ∈ＲＮ的具任意多个结点的径向解的存在性，其中Ｎ＞ ｐ，１＜ ｐ＜ ∞，ｐ＝ ＮｐＮ－ ｐ 为临界Ｓｏｂｏｌｅｖ 指数。所得结果推广了新近Ｃｈａｂｒｏｗ ｓｋｉＪ． 在ｐ＝ ２ 时所得的相应结果。

The existence of nodal radial solutions of the following quasilinear elliptic equation involving critical Sobolev exponent is studied:- div (｜  u｜ p-2  u)=K(｜x｜)｜u｜ p *-2 u,x∈R Nwhere N>p,1<p<∞,p *=NpN-p is the critical Sobolev exponent,and K satisfies certain conditions.This extends the result by Chabrowski J.for p=2 .