| 非线性项依赖于一阶导数的共振情形下二阶三点边值问题解的存在性和唯一性 |
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| 引用本文： | 李晓静,陈绚青,鲁世平.非线性项依赖于一阶导数的共振情形下二阶三点边值问题解的存在性和唯一性[J].应用数学学报,2012,35(2):375-384. |
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| 作者姓名： | 李晓静 陈绚青 鲁世平 |
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| 作者单位： | 1. 江苏技术师范学院数理学院,常州,213001
2. 安徽师范大学数学系,芜湖,241000 |
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| 基金项目： | 江苏省自然科学基金(BK2009105,BK2008119);江苏省高校自然科学基金(09kjd110001,08kjb110011);江苏技术师范学院青年科研基金(KYY08033)资助项目 |
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| 摘 要： | 本文致力于研究共振情形下二阶三点边值问题x″(t)+ f(t,x(t),x'(t))=0, t∈(0,1),x(0)=0, x(1)=ξx(η),其中f:0,1]×R2→R是一个连续函数,ξ＞0,0＜η＜1满足ξn=1.运用先验界估计,微分不等式技巧和Leray-Schauder度理论得到了该边值问题解的存在性和唯一性.
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| 关 键 词： | 非线性边值问题 存在性和唯一性 共振 上下解 Leray-Schauder度 |
Existence and Uniqueness of Three-point Boundary Value Problem at Resonance with Nonlinear Term Depending on the First Order Derivative |
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| LI XIAOJING
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CHEN XUANQING
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LU SHIPING.Existence and Uniqueness of Three-point Boundary Value Problem at Resonance with Nonlinear Term Depending on the First Order Derivative[J].Acta Mathematicae Applicatae Sinica,2012,35(2):375-384. |
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| Authors: | LI XIAOJING CHEN XUANQING LU SHIPING |
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| Institution: | (Department of Mathematics,Anhui Normal University,Wuhu 241000) |
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| Abstract: | This paper is devoted to studying,the second-order three point boundary value problem ar resonance x"(t) + f(t,x(t),x’(t)) =0,t∈(0,1), x(0) = 0,x:(1) =ξx(η), where f:0,1]×R~2→R is continuous,ξ>0,0<η<1 such thatξη=1.The existence and uniqueness of solution of the boundary value problem are given by using priori estimates, differential inequalities technique and Leray-Schauder degree theory. |
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| Keywords: | nonlinear boundary value problem existence and uniqueness resonance upper and lower solutions Leray-Schauder degree |
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