数学物理学报 ›› 2015, Vol. 35 ›› Issue (5): 878-883.

• 论文 • 上一篇    下一篇

一类非线性Volterra方程零解的稳定性

钟越, 袁倩   

  1. 四川师范大学文理学院 成都 610101
  • 收稿日期:2014-11-15 修回日期:2015-04-10 出版日期:2015-10-25 发布日期:2015-10-25
  • 作者简介:钟越,zhongyue1997@126.com
  • 基金资助:

    国家自然科学基金(11301422)资助

The Asymptotic Stability of the Zero Solution for A Nonlinear Volterra Equation

Zhong Yue, Yuan Qian   

  1. The Arts and Sciences College of Sichuan Normal University, Chengdu 610101
  • Received:2014-11-15 Revised:2015-04-10 Online:2015-10-25 Published:2015-10-25

摘要:

讨论如下一类非线性Volterra方程零解的稳定性x'(t)=-a(t)x(t)+b(t)x'(g(t))+0tk(t,s)f(x(s),x(v(s)))ds+h(t),使用不动点理论,并在一定条件下构造适当的压缩映射,得到了方程零解的稳定性.

关键词: 非线性Volterra方程, 压缩映射, 稳定性

Abstract:

The aim of this paper is to deal with the stability of the zero solution for a nonlinear Volterra integro-differential equation x'(t)=-a(t)x(t)+b(t)x'(g(t))+0tk(t,s)f(x(s),x(v(s)))ds+h(t),, The asymptotic stability of the zero solution for the equation is established by using fixed-point theory and constructing contraction mapping.

Key words: Nonlinear Volterra equation, Contraction mapping, Asymptotic stability

中图分类号: 

  • O175.29