有序Banach空间一类四阶边值问题正解的存在性  

The Existence of Positive Solutions for a Class of Fourth-order Boundary Value Problems in Ordered Banach Spaces

作　　者：李小龙[1] 

机构地区：[1]陇东学院数学与统计学院,甘肃庆阳745000

出　　处：《四川师范大学学报（自然科学版）》2013年第3期388-392,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：甘肃省研究生导师计划基金(1110-05)资助项目;陇东学院青年科技创新基金(XYZK1109)资助

摘　　要：一端简单支撑,另一端滑动的弹性梁的形变可以用四阶常微分方程两点边值问题来描述.由于其在物理中的重要性,已有许多人研究了该类问题解的存在性,但这些文献仅限于在一般空间中讨论,并且采用的方法主要是拓扑度及相关的不动点方法与上下解的单调迭代方法,而在Banach空间中只有很少的研究结果.在有序Banach空间中通过非紧性测度的估计技巧与凝聚映射的不动点指数理论,获得了四阶常微分方程两点边值问题正解的存在性结果,其结果推广和改进了一些已有结论.The deformations of an elastic beam in equilibrium state, whose one end is simply supported and the other end sliding, can he described by a fourth-order ordinary differential equation boundary value problem. Owing to its importance in physics, the exist- ence of solutions to this problem has been studied by many authors. But the discussion in existent literature is restricted in general spaces, the methods employed are topological degree and correlative fixed point, and upper and lower solutions monotone iterative, etc. In this paper the problem is discussed in ordered Banach spaces. An existence result of positive solutions for fourth-order boundary val- ue problems is obtatined by employing a new estimate of noncompactness measure and the fixed point index theory of condensing map- ping. The obtained results improve and generalize some known results.

关 键 词：四阶边值问题 闭凸锥 正解 凝聚映射 不动点指数 

分 类 号：O175.15[理学—数学]