Electron. J. Diff. Eqns., Vol. 2008(2008), No. 38, pp. 1-8.

Positive periodic solutions of neutral functional differential equations with a parameter and impulse

Xuanlong Fan, Yongkun Li

Abstract:
In this paper, we consider first-order neutral differential equations with a parameter and impulse in the form of
$$\displaylines{
 \frac{d}{dt}[x(t)-c x(t-\gamma)]=-a(t)g(x(h_1(t)))x(t)+\lambda
 b(t) f\big(x(h_2(t))\big),\quad t\neq t_j;\cr
 \Delta \big[x(t)-c x(t-\gamma)\big]=I_j\big(x(t)\big),\quad
 t=t_j,\; j\in\mathbb{Z}^+.
 }$$
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
  Yongkun Li
Department of Mathematics, Yunnan University
Kunming, Yunnan 650091, China
email: yklie@ynu.edu.cn

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