Banach空间中二阶非线性微分方程无穷边值问题解的存在性  

The Existence of Solutions of Infinite Boundary Value Problems For Second Order Nonlinear Differential Equations in Banach Spaces

作　　者：张海燕[1] 林永[1] 

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《宿州学院学报》2013年第11期72-74,共3页Journal of Suzhou University

基　　金：安徽省教育厅自然科学研究项目"非线性奇异脉冲微分方程组多点边值问题的正解及应用"(KJ2012B187);安徽省教育厅自然科学研究项目"三部图的色唯一性研究"(KJ2008B253)

摘　　要：利用一个比较结果和Mo¨nch不动点定理,研究了Banach空间中一类二阶非线性微分方程无穷边值问题。通过变量代换,将二阶非线性微分方程边值问题转化为一阶非线性方程组无穷边值问题,在非线性项满足一定的增长性条件下,结合范数定义和不动点理论,获得了解的存在性定理。所得结果改进了某些已知的结论,最后给出了具体应用实例。By using a new comparison result and applying the Monch fixed theorem,the existence of solutions of infinite boundary value problems for nonlinear second order differential equations is investigated. Applying variable substitution, the infinite boundary value problems for nonlinear second order differential equations is reduced to the infinite boundary value problems for nonlinear first order systems, the existence theorem of solutions is established combining with the fixed point theorem and definition of norm, when nonlinear terms satisfying some growth conditions. The results in this paper improve some known results. As for application, we give a example to demonstrate our results.

关 键 词：比较结果 边值问题 不动点定理 BANACH空间 

分 类 号：O177.91[理学—数学]