一类半线性椭圆型方程组正解的存在性与不存在性  

Nonexistence and Existence of Positive Solutions of Semilinear Elliptic Systems

作　　者：朱立平[1] 张正策[2] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710054 [2]西安交通大学理学院,陕西西安710049

出　　处：《南京师大学报（自然科学版）》2006年第1期25-29,共5页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：西安交通大学自然科学基金;国家自然科学基金资助项目(10426027;10571022)

摘　　要：通过Kelvin变换,对移动平面法作了重要的改进和简化,利用移动球面法证明了一类半线性椭圆型方程组古典正解的存在性与不存在性定理;移动球面法并不需要方程组的极大值原理,推广了应用积分法得到的结果,而且还证明了临界情形时古典正解的确切形式;此外,移动球面法也容易推广应用到一般非线性椭圆方程(组)的L iouville问题.In this paper, we introduce the Kelvin transforms and apply the method of moving spheres which is the significant simplifications of moving plane method to prove the existence and nonexistence of positive solutions for a class of semilinear elliptic systems. The method of moving spheres doesnt not need the maximum principle for elliptic systems and obtains the exact form of positive solutions for the critical case which extends the results proved by the integral method. Moreover, this method is also used to prove the Liouville theorems for the general nonlinear elliptic equations or systems.

关 键 词：存在性 不存在性 移动球面法 

分 类 号：O175.25[理学—数学]