Second-Order Impulsive Differential Equations with Functional Initial Conditions on Unbounded Intervals

Abstract

We present some results on the existence of solutions for second-order impulsive differential equations with deviating argument subject to functional initial conditions. Our results are based on Schaefer's fixed point theorem for completely continuous operators.

Nonnegative solutions for a system of impulsive BVPs with nonlinear nonlocal BCs

“…In the case of impulsive equations, nonlocal BCs have been studied by many authors, see for example [5,6,8,13,14,18,31,32,39,56] and references therein. The functions H i , L i are continuous functions; for earlier contributions on problems with nonlinear BCs we refer the reader to [9,10,16,17,21,24,43,45] and references therein. Our idea is to start from the results of [26,27], valid for non-impulsive systems, and to rewrite the system (1.1)-(1.3) as a system of perturbed Hammerstein integral equations, namely…”

“…In the case of impulsive equations, nonlocal BCs have been studied by many authors, see for example [5,6,8,13,14,18,31,32,39,56] and references therein. The functions H i , L i are continuous functions; for earlier contributions on problems with nonlinear BCs we refer the reader to [9,10,16,17,21,24,43,45] and references therein.…”