数学季刊 >

2014 , Vol. 29 >Issue 2: 203 - 209

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.02.007

共振条件下2k阶微分方程周期边值问题解的存在唯一性

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  • Department of Mathematics,Changzhou Institute of Technology
FENG Yan-qing(1969-), female, native of Yiwu, Zhejiang, an associate professor of Changzhou Institute of Technology, M.S.D., engages in nonlinear function analysis and application; WANG Zhong-ying(1968-), female, native of Changzhou, Jiangsu, an associate professor of Changzhou Institute of Technology, M.S.D., engages in nonlinear function analysis.

收稿日期: 2012-06-18

  网络出版日期: 2021-01-25

基金资助

Supported by the Natural Science Foundation of Changzhou Instituty of Technology（YN09090）； Supported by the Natural Science Foundation of Jiangsu Province（13KJD110001）；

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The Existence and Uniqueness of the Solution for Periodical Boundary Value Problems of 2kth Order Differential Equations with Resonance

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  • Department of Mathematics,Changzhou Institute of Technology
FENG Yan-qing(1969-), female, native of Yiwu, Zhejiang, an associate professor of Changzhou Institute of Technology, M.S.D., engages in nonlinear function analysis and application; WANG Zhong-ying(1968-), female, native of Changzhou, Jiangsu, an associate professor of Changzhou Institute of Technology, M.S.D., engages in nonlinear function analysis.

Received date: 2012-06-18

  Online published: 2021-01-25

Supported by

Supported by the Natural Science Foundation of Changzhou Instituty of Technology（YN09090）； Supported by the Natural Science Foundation of Jiangsu Province（13KJD110001）；

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摘要

In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems. 

关键词： initial value problem; global homeomorphism; periodic solution; nonnegative auxiliary scalar coercive function; resonance

本文引用格式

冯艳青, 王忠英 . 共振条件下2k阶微分方程周期边值问题解的存在唯一性[J]. 数学季刊, 2014 , 29(2) : 203 -209 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.02.007

Abstract

In this paper, a new set of sufficient conditions related to an initial value problem and global homeomorphism is obtained in discussing the existence and uniqueness of 2π-periodic solution for 2kth order differential equations with resonance. The key role is played by nonnegative auxiliary scalar coercive function. The result of this paper generalizes some existed theorems. 

Key words： initial value problem; global homeomorphism; periodic solution; nonnegative auxiliary scalar coercive function; resonance

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