Existence Results for Impulsive Systems with Initial Nonlocal Conditions

Abstract

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.

Keywords:

• impulsive differential system
• nonlocal initial condition
• vector norm
• convergent to zero matrix

AMS Subject Classification:

• 34A37
• 34A12
• 34B10
• 47H10