×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: EMIS EuDML