MULTIPLE AND SIGN-CHANGING SOLUTIONS FOR NONLINEAR ELLIPTIC EQUATION WITH CRITICAL POTENTIAL AND CRITICAL PARAMETER

被引：0
|
作者：
王友军 [1 ]
沈尧天 [1 ]
机构：
[1] School of Mathematical Sciences,South China University of Technology
来源：
ActaMathematicaScientia | 2010年 / 30卷 / 01期
基金：
美国国家科学基金会;
关键词：
nonlinear elliptic equation; critical potential; linking;
D O I：
暂无
中图分类号：
O175.25 [椭圆型方程];
学科分类号：
070104 ;
摘要：
Some embedding inequalities in Hardy-Sobolev space are proved.Furthermore,by the improved inequalities and the linking theorem,in a new k-order Sobolev-Hardy space,we obtain the existence of sign-changing solutions for the nonlinear elliptic equation {-△（k）u:=-△u-（（（N-2）2）/4）U/︱X︱2-1/4 sum from i=1 to（k-1） u/（︱x︱2（In（i）R/︱x︱2））=f（x,u）,x ∈Ω,u=0,x ∈Ω,where 0 ∈ΩBa（0）RN,N≥3,ln（i）=i éj=1 ln（j）,and R=ae（k-1）,where e（0）=1,e（j） = ee（j-1） for j≥1,ln（1）=ln,ln（j）=ln ln（j-1） for j≥2.Besides,positive andnegative solutions are obtained by a variant mountain pass theorem.
引用
收藏
页码：113 / 124
页数：12
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