In this paper, we consider first-order neutral differential equations with a parameter and impulse in the form of
![$$\displaylines{
\frac{d}{dt}[x(t)-c x(t-\gamma)]=-a(t)g(x(h_1(t)))x(t)+\lambda
b(t) f\big(x(h_2(t))\big),\quad t\neq t_j;\cr
\Delta \big[x(t)-c x(t-\gamma)\big]=I_j\big(x(t)\big),\quad
t=t_j,\; j\in\mathbb{Z}^+.
}$$](gifs/aa.gif)
Leggett-Williams fixed point theorem, we prove the existence of three positive periodic solutions.
Xuanlong Fan, Yongkun Li
Abstract:
In this paper, we consider first-order neutral differential
equations with a parameter and impulse in the form of
Leggett-Williams fixed point
theorem, we prove the existence of three positive periodic solutions.
Submitted December 16, 2007. Published March 14, 2008.
Math Subject Classifications: 34K13, 34K40.
Key Words: Periodic solution; functional differential equation;
fixed point; cone.
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Xuanlong Fan Department of Mathematics, Yunnan University Kunming, Yunnan 650091, China email: fanxuanlong@126.com |
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| Yongkun Li Department of Mathematics, Yunnan University Kunming, Yunnan 650091, China email: yklie@ynu.edu.cn |
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