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Existence results for impulsive neutral functional differential inclusions. (English) Zbl 1089.34064

Existence results are obtained for the following first-order nonlinear neutral inclusions with impulses \[ \begin{aligned}\frac{d}{dt}[x(t)-f(t,x_t)]\in G(t,x_t)&\quad \text{a.e. }t\in [0,T], \;t\neq t_k,\;k=1,\dots,m,\\ x(t_k^{+})-x(t_k^{-})=I_k(t_k^{+}),&\quad k=1,\dots,m,\;x_0=\phi,\end{aligned} \] and for similar second-order inclusions.

MSC:

34K45 Functional-differential equations with impulses
34K40 Neutral functional-differential equations
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