一类半线性椭圆型方程组边值问题的可解性  

Solvability of a class of semi-linear elliptic equations boundary value

作　　者：金启胜[1,2] 周宗福[3] Jin Qisheng Zhou Zongfu(Anqing Normal University, Anqing Vocational and Technical College, Anqing 246003, China School of Mathematics Science,Anhui University, Hefei 230039, China)

机构地区：[1]安庆师范大学 [2]安庆职业技术学院,安徽安庆246003 [3]安徽大学数学科学学院,安徽合肥230039

出　　处：《纯粹数学与应用数学》2017年第3期248-253,共6页Pure and Applied Mathematics

基　　金：安徽省教育厅项目(2015jyxm539);安徽省自然科研项目(KJ2016A447)

摘　　要：利用极大值原理和Holder,Poincare不等式,证明了一类半线性椭圆型方程组解的非负性和唯一性.在此基础上,又利用连续统理论证明了该边值问题有且仅有唯一的正解,推广了该边值问题可解性的结论.In this paper, we proved the non-negativity and uniqueness of the solution to a class of semilinear elliptic equations with the maximum principle and Holder and Poincare inequality. On the basis of this theory, we prove that the boundary-value problem has only one positive solution according to continuum theory, generalizing the conclusion of the solvability of boundary-value problem.

关 键 词：连续统 紧正算子 极大值原理 正解 

分 类 号：O175.2[理学—数学]