共振条件下2k阶微分方程周期边值问题解的存在唯一性

doi:10.13371/j.cnki.chin.q.j.m.2014.02.007

数学季刊 ›› 2014, Vol. 29 ›› Issue (2): 203-209.doi: 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

Department of Mathematics,Changzhou Institute of Technology

收稿日期:2012-06-18 出版日期:2014-06-30 发布日期:2021-01-25
作者简介: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.
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）；

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

Department of Mathematics,Changzhou Institute of Technology

Received:2012-06-18 Online:2014-06-30 Published:2021-01-25
About author: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.
Supported by:
Supported by the Natural Science Foundation of Changzhou Instituty of Technology（YN09090）； Supported by the Natural Science Foundation of Jiangsu Province（13KJD110001）；

摘要/Abstract

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

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

中图分类号:

O175.8

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.

FENG Yan-qing, WANG Zhong-ying. The Existence and Uniqueness of the Solution for Periodical Boundary Value Problems of 2kth Order Differential Equations with Resonance[J]. Chinese Quarterly Journal of Mathematics, 2014, 29(2): 203-209.

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共振条件下2k阶微分方程周期边值问题解的存在唯一性

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

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