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

Tom 97 / 2010

Yongkun Li, Changzhao Li, Juan Zhang Annales Polonici Mathematici 97 (2010), 169-183 MSC: Primary 34K13; Secondary 34K32. DOI: 10.4064/ap97-2-6

Streszczenie

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.

Autorzy

  • Yongkun LiDepartment of Mathematics
    Yunnan University
    Kunming, Yunnan 650091
    People's Republic of China
    e-mail
  • Changzhao LiDepartment of Mathematics
    Yunnan University
    Kunming, Yunnan 650091
    People's Republic of China
  • Juan ZhangDepartment of Mathematics
    Yunnan University
    Kunming, Yunnan 650091
    People's Republic of China

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