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Multiple solutions for nonresonance impulsive functional differential equations. (English) Zbl 1047.34095
The authors obtain sufficient conditions for the existence at least three solutions of the following first-order impulsive functional-differential equation $y'(t)-\lambda y(t)=f(t,y_t), \text{ a.e.} \quad t\in [0,T],\;t\neq t_k,\;k=1,2,\dots,m,$
$\Delta y| _{t=t_k} =I_k(y(t_k^{-})), \quad k=1,2,\dots,m,$
$y(t)=\phi(t),\quad t\in[-r,0],\qquad y(0)=y(T)$ and of a similar second order impulsive functional-differential equation. For existence results, they apply the Leggett-Williams fixed-point theorem.
##### MSC:
 34K45 Functional-differential equations with impulses
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