Three periodic solutions for a class of higher-dimensional functional differential equations with impulses

Yongkun Li¹ ; Changzhao Li¹ ; Juan Zhang¹

¹ Department of Mathematics Yunnan University Kunming, Yunnan 650091 People's Republic of China

Annales Polonici Mathematici, Tome 97 (2010) no. 2, pp. 169-183.

Résumé

By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of $n$-dimensional functional differential equations with impulses of the form $$ \left\{ \eqalign{ y'(t)=A(t)y(t)+g(t,y_{t}), \quad \hbox{$t\neq t_{j}$,}\hskip2.3pt j\in\mathbb{Z}, \cr y(t_{j}^{+})=y(t_{j}^{-})+I_{j}(y(t_{j})),\cr} \right. $$ where $A(t)=(a_{ij}(t))_{n\times n}$ is a nonsingular matrix with continuous real-valued entries.

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DOI : 10.4064/ap97-2-6

Keywords: using well known leggett williams multiple fixed point theorem cones criteria established existence three positive periodic solutions class n dimensional functional differential equations impulses form eqalign t quad hbox neq hskip mathbb right where times nonsingular matrix continuous real valued entries