Geodesic
Positive periodic solutions of neutral functional differential equations with a parameter and impulse
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34K13, 34K40
Keywords: periodic solution, functional differential equation, fixed point, cone 
@article{EJDE_2008__2008__a57,
     author = {Fan, Xuanlong and Li, Yongkun},
     title = {Positive periodic solutions of neutral functional differential equations with a parameter and impulse},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2008},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a57/}
}
TY  - JOUR
AU  - Fan, Xuanlong
AU  - Li, Yongkun
TI  - Positive periodic solutions of neutral functional differential equations with a parameter and impulse
JO  - Electronic Journal of Differential Equations
PY  - 2008
VL  - 2008
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a57/
LA  - en
ID  - EJDE_2008__2008__a57
ER  - 
%0 Journal Article
%A Fan, Xuanlong
%A Li, Yongkun
%T Positive periodic solutions of neutral functional differential equations with a parameter and impulse
%J Electronic Journal of Differential Equations
%D 2008
%V 2008
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a57/
%G en
%F EJDE_2008__2008__a57
Fan, Xuanlong; Li, Yongkun. Positive periodic solutions of neutral functional differential equations with a parameter and impulse. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a57/