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Existence results for impulsive systems with initial nonlocal conditions. (English) Zbl 1301.34017
Summary: We study the existence of solutions for nonlinear first order impulsive systems with nonlocal initial conditions. Our approach relies in the fixed point principles of Schauder and Perov, combined with a vector approach that uses matrices that converge to zero. We prove existence and uniqueness results for these systems. Some examples are presented to illustrate the theory.

34A37 Ordinary differential equations with impulses
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
47H10 Fixed-point theorems
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