一类n阶完全常微分方程边值问题解的存在性

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英文篇名：Existence of Solution for a Class of Fully n-th Order Ordinary Differential Boundary Value Problem 作者：李菊鹏 ; 李永祥 英文作者：LI Jupeng;LI Yongxiang;College of Mathematics and Statistics,Northwest Normal University; 关键词：完全n阶边值问题 ; 超线性增长 ; Nagumo型增长条件 ; Leray-Schauder不动点定理 英文关键词：fully n-th order boundary value problem;;superlinear growth;;Nagumo-type growth condition;;Leray-Schauder fixed point theorem 中文刊名：JLDX 英文刊名：Journal of Jilin University(Science Edition) 机构：西北师范大学数学与统计学院; 出版日期：2019-01-26 出版单位：吉林大学学报(理学版) 年：2019 期：v.57;No.235 基金：国家自然科学基金(批准号:11261053;11661071) 语种：中文; 页：JLDX201901003 页数：6 CN：01 ISSN：22-1340/O 分类号：15-20

摘要

用Leray-Schauder不动点定理,讨论完全n阶边值问题:{-u~((n))(t)=f(t,u(t),u′(t),…,u~((n-1))(t)), t∈[0,1],u~((i))(0)=0, i=0,1,2,…,n-2,u~((n-1))(1)=0烅烄烆解的存在性,其中f:[0,1]×R~n→R为连续函数.在一个允许f(t,x_0,x_1,…,x_(n-1))关于x_i(i=0,1,2,…,n-1)超线性增长的不等式条件及f(t,x_0,x_1,…,x_(n-1))关于x_(n-1)满足Nagumo型增长的条件下,得到了该问题解的存在性.
        Using the Leray-Schauder fixed point theorem,we discussed the existence of solutions for a class of fully n-th order boundary value problem:{-u~((n))(t)=f(t,u(t),u′(t),…,u~((n-1))(t)), t∈ [0,1],u~((i))(0)=0, i=0,1,2,…,n-2,u~((n-1))(1)=0.Where f:[0,1]×R~n→R was a continuous function.The existence of solutions was obtained under a inequality condition that allowed f(t,x_0,x_1,…,x_(n-1))is superlinear growth on x_i(i=0,1,2,…,n-1)and f(t,x_0,x_1,…,x_(n-1))satisfied the Nagumo-type growth condition on x_(n-1).

引文

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