一类超临界椭圆方程组正解的存在性  

Existence of Positive Solutions for a Class of Supercritical Elliptic Equations

作　　者：康晓红[1] 樊永生[2] 

机构地区：[1]深圳职业技术学院数理部,深圳518055 [2]中北大学计算机与控制工程学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2015年第3期272-275,281,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(31100958)

摘　　要：讨论了n≥3维球域上具零边值的一类椭圆方程组,Henon型椭圆方程组,它是Lane-Emden方程组的变形,即其主要非线性项各有一个在球心取零值的对称权重.通过建立对称Sobolev函数空间到加权Lp空间的嵌入定理,证明存在一条关于所论方程组非线性项指数(p,q)的双曲线,称为Henon双曲线,它位于临界Hardy-Littlewood-Sobolev曲线上方,使得对于Henon双曲线下方的点(p,q),方程组具有一组非平凡解.A class of partial elliptic systems,Henon systems with zero boundary condition is considered on a ball of dimension n≥3,which is a modification of Lane-Emden systems,added to its main nonlinear term with a radially symmetric weight with zero value at the origin of the ball.Through establishing a imbedding theorem between symmetric Sobolev function and weighted Lp spaces,a hyperbola which called Henon hyperbola with variable（p,q）,which is the exponents of main nonlinear terms of the Henon system was existed.It was lying above the critical Hardy-Littlewood-Sobolev hyperbola,and the Henon system has a group of non-trivial solutions for（p,q）under this curve.

关 键 词：临界双曲线 椭圆方程组 强不定型 临界点 

分 类 号：O175.25[理学—数学]