一类奇异拟线性椭圆方程组正解的存在性  

Positive Solutions for a Class of Quasilinear Singular Elliptic Systems

作　　者：王雨婷 贾高[1] WANG Yuting;JIA Gao(College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2018年第4期307-311,322,共6页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11171220);上海市一流学科(系统科学)建设项目(XTKX2012)

摘　　要：在有C^(1,α)边界的有界区域中,研究了一类奇异拟线性椭圆方程组正解的存在性。对于这类方程组具有3个负指数即有奇异性的情形,以往处理半线性椭圆方程组的Morse理论、上下解方法、极小极大方法等传统方法不可以直接使用,因此,对于这类拟线性椭圆方程组,首先基于上下解理论在指数满足一定条件下构造方程组的上下解,再根据所得上下解定义集合,然后在对应的集合里验证定义的算子满足Schaulder不动点定理的相关条件,最后根据不动点定理获得这类奇异拟线性椭圆方程组的正解。In the bounded domain with C1,Qr boundary,the existence of positive solutions for a class of quasilinear singular elliptic system was studied.For such system with three negative exponents,that is,a singular system,the traditional methods,such as the Morse theory,the theory of sub-and super-solutions and minimax methods,which are used usually to deal with semilinear elliptic systems in the past,can not be used directly.So,for this kind of quasilinear elliptic systems,sub-and super-solutions of the system were first constructed on the basis of the sub-and super-solution theory.Next,a set was defined according to the obtained sub-and super-solutions,and it was verified that in the corresponding set the defined operator satisfies the related conditions of the sufficient Schaulder fixed point theorem.Then,the positive solutions of the quasilinear singular elliptic system were obtained according to the fixed point theorem.

关 键 词：拟线性椭圆方程 奇异性 上下解方法 弱解 

分 类 号：F830[经济管理—金融学]