共振情形下周期边值问题正解的全局分歧

闫东明

系统科学与数学 ›› 2014, Vol. 34 ›› Issue (8) : 935-949.

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PDF(342 KB)
系统科学与数学 ›› 2014, Vol. 34 ›› Issue (8) : 935-949. DOI: 10.12341/jssms12389
论文

共振情形下周期边值问题正解的全局分歧

    闫东明
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GLOBAL BIFURCATION OF POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS AT RESONANCE

    YAN Dongming
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摘要

虑共振情形下二阶常微分方程周期边值问题 {u=f(t,u),   t(0,2π),u(0)=u(2π),  u(0)=u(2π)  正解的全局分歧, 其中~f:[0,2π]×RR\ (R=(,+)) 为连续函数. 运用~Dancer 全局分歧定理获得了上述问题至少存在一个正解的若干充分条件, 这些充分条件中所涉及的值是最优的.

Abstract

In this paper, we are concerned with the global bifurcation of positive solutions for the following second order periodic boundary value problem {u=f(t,u),    t(0,2π),u(0)=u(2π),  u(0)=u(2π),  where~f:[0,2π]×RR~(R=(,+)) is continuous. By using Dancer's global bifurcation theorem, we obtain some optimal conditions such that the above problem has at least one positive solution.

关键词

周期边值问题 / 共振 / Dancer 全局分歧定理 / 主特征值 / 正解.

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闫东明. 共振情形下周期边值问题正解的全局分歧. 系统科学与数学, 2014, 34(8): 935-949. https://doi.org/10.12341/jssms12389
YAN Dongming. GLOBAL BIFURCATION OF POSITIVE SOLUTIONS OF PERIODIC BOUNDARY VALUE PROBLEMS AT RESONANCE. Journal of Systems Science and Mathematical Sciences, 2014, 34(8): 935-949 https://doi.org/10.12341/jssms12389
中图分类号: 34B15    34B18   
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