非线性三阶常微分方程的多点边值正解问题探索  

Exploration for Multipoint Boundary Value Positive Solutions of Nonlinear Third Order Ordinary Differential Equations

作　　者：何林海 HE Lin-hai(Xiangtan Medicine & Health Vocational College,Xiangtan 411102,China)

机构地区：[1]湘潭医卫职业技术学院,湖南湘潭411102

出　　处：《山东农业大学学报（自然科学版）》2019年第2期346-349,共4页Journal of Shandong Agricultural University：Natural Science Edition

摘　　要：针对非线性三阶常微分方程多点边值正解问题研究较少的现状,本文以锥上不动点定理为基础,构建相应的等价方程,证明非线性三阶常微分方程存在正解的可能性。计算结果表明:在Banach空间X的锥K中,当条件(H)成立,若(H1)成立,则至少存在3个正解;若条件(H2)成立,则至少存在2个正解;若条件(H3)、(H4)成立,则存在至少1个正解。相对于已有文献的研究结果,本文的解法有一定的创新价值。In view of the current situation that there are few studies on positive solutions of multi-point boundary value of third-order non-linear ordinary differential equations,this paper constructs corresponding equivalent equations on the basis of fixed point theorem on cone,and proves the possibility of existence of positive solutions of third-order non-linear ordinary differential equations.The results show that:in the cone K of Banach space X,if condition(H)holds and(H1)holds,there are at least three positive solutions;If condition(H2)holds,there are at least two positive solutions,and if condition(H3)and(H4)holds,there is at least one positive solution.Compared with the research results in the existing literature,the solution in this paper has some innovative value.

关 键 词：三阶常微分方程 非线性 多点边值 正解 

分 类 号：O175.14[理学—数学]