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On first-order initial value problems for impulsive differential inclusions in Banach spaces. (English) Zbl 0929.34017

The paper concerns the existence of solutions \(y:[0,T]\to E\) to the problem \(y'(t)\in F(t,y(t))\), \(y(t^+_k)=I_k(y(t^-_k))\), \(y(0)=0\). Here, \(E\) is a Banach space and the result extends the scalar problem considered by M. Frigon and D. O’Regan [J. Math. Anal. Appl. 193, No. 1, 96-113 (1995; Zbl 0853.34011)].
Reviewer: C.Ursescu (Iaşi)

MSC:

34A60 Ordinary differential inclusions
34A37 Ordinary differential equations with impulses
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces

Citations:

Zbl 0853.34011