EXISTENCE AND REGULARITY OF POSITIVE SOLUTIONS OF THE ELLIPTIC EQUATIONS INVOLVING CRITICAL NONLINEAR AND SUBLINEAR  

作　　者：刘宪高 

机构地区：[1]Dept.of Math.,University of Hunan,Changsha 410012

出　　处：《四川师范大学学报（自然科学版）》1991年第1期45-46,共2页Journal of Sichuan Normal University（Natural Science）

摘　　要：0 IntroductionLet Ωbe a smooth bounded domain in Rⁿ with n】3, consider the problem of finding a function u（x）which satisfieswhere 0【α【1, 1【P=2ⁿ-1, 2ⁿ=2n/n-2 is the critical exponent for Sobolev embedding H₀¹→L².Indeed solutions of （0 ,1） correspond to critical points of the functionalBrezis and Nirenberg considered the case α≥1 and p= 2^* -1, and obtainedTheorem （B , N） Let n≥4, when α=1 and 0 【λ【 λ₁,there is a solution of （0. 1） ; when α】 1 there is asolution of （0. 1） for any λ】0.The principal tecncihique of argument in [1] is using positive radial solution （0. 3） of equation -△u=u²ⁿ-1 in R^*.

关 键 词：NIRENBERG ARGUMENT embedding correspond EXPONENT finding radial satis 下尸 false 

分 类 号：N55，G658.3[自然科学总论]