Existence result for impulsive coupled systems on the half-line

  • Feliz Minhós
  • Robert de Sousa
Original Paper


This work considers a second order impulsive coupled system of differential equations with generalized jump conditions in half-line, which can depend on the impulses of the unknown functions and their first derivatives. The arguments apply the fixed point theory, Green’s functions technique, \(L^{1}\)-Carathéodory functions and sequences and Schauder’s fixed point theorem. The method is based on Carathéodory concept of functions and sequences, together with the equiconvergence on infinity and on each impulsive moment, and it allows to consider coupled fully nonlinearities and very general impulsive functions.


Coupled systems \(L^{1}\)-Carathéodory functions Green’s functions Equiconvergence at infinity and at the impulsive points Schauder’s fixed-point theorem Problems on the half-line 

Mathematics Subject Classification

34B15 34B27 34L30 92B05 


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Copyright information

© Springer-Verlag Italia S.r.l., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática, Escola de Ciências e Tecnologia, Centro de Investigação em Matemática e Aplicaçõ es (CIMA), Instituto de Investigação e Formação AvançadaUniversidade de ÉvoraÉvoraPortugal
  2. 2.Faculdade de Ciências e Tecnologia, Núcleo de Matemática e Aplicações (NUMAT)Universidade de Cabo VerdePraiaCabo Verde

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