Benchohra, Mouffak; Boucherif, Abdelkader On first-order initial value problems for impulsive differential inclusions in Banach spaces. (English) Zbl 0929.34017 Dyn. Syst. Appl. 8, No. 1, 119-126 (1999). 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) Cited in 5 Documents 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 Keywords:first-order initial value problems; impulsive differential inclusions Citations:Zbl 0853.34011 × Cite Format Result Cite Review PDF