Three periodic solutions for a class of higher-dimensional functional differential equations with impulses
Volume 97 / 2010
Annales Polonici Mathematici 97 (2010), 169-183
MSC: Primary 34K13; Secondary 34K32.
DOI: 10.4064/ap97-2-6
Abstract
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.
