Robin型无穷多点边值问题正解的存在性  

Beingness of the Positive Solutions for ∞-Point Boundary Value Problems of Robin Type

作　　者：覃仕霞[1] 罗圆[2] 

机构地区：[1]成都信息工程学院应用数学学院,成都610225 [2]西南交通大学土木工程学院,成都610031

出　　处：《四川理工学院学报（自然科学版）》2015年第3期90-95,共6页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11171046)

摘　　要：通过利用锥上不动点定理,讨论了二阶Robin型无穷多点边值问题正解的存在性。首先利用一个线性方程的特解构造新的Green函数,进而证明了Robin型无穷多点边值问题的微分方程等价于一个简单的积分方程;最后利用不动点定理研究此积分方程,并推导出原Robin型无穷多点边值问题在满足条件0≤f+0<M1,m1<f-∞≤∞或0≤f+∞<M1,m1<f-0≤∞时,至少存在一个正解。主要结果改进和推广了无穷多点边值问题的相关结论。The existence of positive solutions for the second order ∞-point boundary value problems of Robin type was discussed through using the fixed point theorem in cone. Firstly,the special solution of a linear equation was used to construct a new Green function,and then,the differential equation of the ∞-point boundary value problems of Robin type was proved that it is equivalent to a simple integral equation. Finally,the integral equation was studied through using the fixed point theorem and the ∞-point boundary value problems of Robin type mentioned above was derived that there at least exists one positive solution if the condition of 0≤f0^＋〈M1,m1〈f∞^-≤∞ or 0≤f∞^＋〈M1,m1〈f0^-≤∞ is met. The main results presented in this paper improved and generalized some relevant results of ∞-point boundary value problems of Robin type.

关 键 词：常微分方程 Robin型无穷多点边值问题 等价积分方程 正解 不动点定理 

分 类 号：O29[理学—应用数学]