非线性项变号的脉冲微分方程正解的存在性

J4 ›› 2010, Vol. 45 ›› Issue (12): 83-87.

非线性项变号的脉冲微分方程正解的存在性

姚林红¹, 赵爱民²

1.中北大学理学院, 山西太原 030051; 2.山西大学数学科学学院, 山西太原 030006

收稿日期:2010-01-09 出版日期:2010-12-16 发布日期:2011-03-16
作者简介:姚林红(1982-), 女,博士研究生,助教,研究方向为动力系统. Email:yaolinhong@mail.bnu.edu.cn
基金资助:
山西省自然科学基金资助项目 (2009011005-1)

Existence of positive solutions for an impulsive differential equation with a sign changing nonlinear term

YAO Lin-hong¹, ZHAO Ai-min²

1. School of Sciences, North University of China, Taiyuan 030051, Shanxi, China;
2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China

Received:2010-01-09 Online:2010-12-16 Published:2011-03-16

摘要/Abstract

摘要：

利用锥上的不动点指数理论得到了f变号时脉冲微分方程边值问题
           -y″(t)=f(t,y(t)), t∈［0,1］＼｛t₁,t₂,…,t_m｝,
             Δy′(tk)=J_k(y(t_k)), k=1,…,m,
             y(0)=y(1)=0
正解的存在性,本文的结果推广并改进了相关文献的结论。

关键词: 边值问题;不动点指数;脉冲微分方程

Abstract:

The existence of positive solutions are obtained for boundary value problems of impulsive differential equation
           -y″(t)=f(t,y(t)), t∈［0,1］＼｛t₁,t₂,…,t_m｝,
             Δy′(tk)=J_k(y(t_k)), k=1,…,m,
             y(0)=y(1)=0
where f can change the sign. The proof is based on the fixed point index theorem in cones. The results of this paper improve and generalize the known results in the literature.

Key words: boundary value problem; fixed point index; impulsive differential equation

姚林红1, 赵爱民2. 非线性项变号的脉冲微分方程正解的存在性[J]. J4, 2010, 45(12): 83-87.

YAO Lin-hong1, ZHAO Ai-min2. Existence of positive solutions for an impulsive differential equation with a sign changing nonlinear term[J]. J4, 2010, 45(12): 83-87.

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