华东师范大学学报(自然科学版) ›› 2007, Vol. 2007 ›› Issue (1): 7-12.

• 数学 • 上一篇    下一篇

时间尺度上二阶动力方程的特征值问题(英）

耿凤杰, 朱德明   

  1. 华东师范大学 数学系, 上海 200062
  • 收稿日期:2005-09-17 修回日期:2006-03-17 出版日期:2007-01-25 发布日期:2007-01-25
  • 通讯作者: 耿凤杰

Eigenvalue Problems for Second-order Dynamic Equations on Time Scales(English)

GENG Feng-jie, ZHU De-ming   

  1. Department of Mathematics , East China Normal University , Shanghai 200062, China
  • Received:2005-09-17 Revised:2006-03-17 Online:2007-01-25 Published:2007-01-25
  • Contact: GENG Feng-jie

摘要： 讨论了时间尺度上非线性二阶动力方程的特征值问题，该问题满足 m 点边界条件. 利用 Schauder 及 Krasnoselskii 不动点定理刻画了其特征值，给出了正解存在性结果. 还得到了特征值 λ 的具体的区间，使得在这些区间里 所讨论的边值问题至少 有一个正解存在.

关键词: 时间尺度, 跳跃算子, m 点边值问题, 二阶动力方程, 锥, 时间尺度, 跳跃算子, m 点边值问题, 二阶动力方程, 锥

Abstract: The paper studied the eigenvalue problems for nonlinear second-order dynamic equations on time scales with m-point boundary conditions. Using Schauder's
and Krasnoselskii's fixed point theorems, the eigenvalues were characterized and the existence of positive solutions established. Several kinds of intervals of
λ were presented explicitly, in which the existence of at least one positive solution of BVP was guaranteed.

Key words: jump operators, m-point boundary value problem, second-order dynamic equations, cone , time scales, jump operators, m-point boundary value problem, second-order dynamic equations, cone

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