摘要
本文讨论了一类共形不变摄动积分方程正解的存在性.我们证明了:当参数对(p,q)属于集合(n,0)×(0,∞)且pq+p+2n=0时,对应摄动积分方程存在正解;而当参数对(p,q)属于集合(0,∞)×(∞,0)也满足pq+p+2n=0时,摄动积分方程不存在非负解.这与原共形不变积分方程有着本质的不同,此结果隐含着这类积分方程正解的存在性取决于解在无穷远处的性态.
In this article,the existence of non-negative solution to a perturbed conformal invariant integral equation was studied.As p ∈（n,0）,q 0 such that pq ＋ p ＋ 2n = 0,the existence of non-negative solutions to perturbed integral equation is established,however as p ∈（0,∞）,q 0 such that pq ＋ p ＋ 2n = 0,we show the perturbed integral equation has not non-negative solutions,which is different from the original conformal invariant integral equation and denotes the existence of integral equation is determined by the behavior of solution near infinity.
出处
《中国科学：数学》
CSCD
北大核心
2012年第4期329-340,共12页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:10976026,1107120)
国家自然科学基金专项基金-天元基金(批准号:11126148)
福建省自然科学基金(批准号:2010J01013)
湖南省农业大学大学生创新性试验计划(批准号:XCX1122)资助项目
