Benchohra, M.; Henderson, J.; Ntouyas, S. K.; Ouahab, A. Existence results for impulsive semilinear damped differential inclusions. (English) Zbl 1046.34017 Electron. J. Qual. Theory Differ. Equ. 2003, Paper No. 11, 19 p. (2003). The paper deals with the existence of mild solutions for first-order impulsive semilinear evolution inclusions \(y'-Ay \in By+ F(t,y)\), \(t\in [0,b]\setminus \{t_1, \dots ,t_m\}\), where \(F :[0,b]\times E \to E\) (\(E\) is a separable Banach space) is a multivalued map, \(A\) is the infinitesimal operator of a semigroup of linear operators and \(B\) is a bounded operator from \(E\) into \(E\). The second-order impulsive semilinear evolution equation \(u''+Ay \in By'+F(t,y)\), where \(B\) and \(F\) be as above and \(A\) is the infinitesimal operator of a cosine family is also considered. The multivalued map \(F\) can be convex- or nonconvex-valued. In the first case, the proof is based on the Bohnenblust/Karlin fixed-point theorem, in the second case on the Covitz/Nadler fixed-point theorem. Reviewer: Jozef Myjak (L’Aquila) Cited in 5 Documents MSC: 34A37 Ordinary differential equations with impulses 34A60 Ordinary differential inclusions 34G20 Nonlinear differential equations in abstract spaces 35R10 Partial functional-differential equations 47H20 Semigroups of nonlinear operators Keywords:Impulsive damped differential inclusions; Banach spaces; infinitesimal operators; semigroups; cosine operators; fixed-points. PDFBibTeX XMLCite \textit{M. Benchohra} et al., Electron. J. Qual. Theory Differ. Equ. 2003, Paper No. 11, 19 p. (2003; Zbl 1046.34017) Full Text: EuDML EMIS