Geodesic
Existence results for systems of second-order impulsive differential equations
J. R. Graef1 ; H. Kadari2 ; A. Ouahab2 ; A. Oumansour3 ; J. R. Graef ; H. Kadari ; A. Ouahab ; A. Oumansour
1Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, USA
2Laboratoire de Biomathematiques Universite Djillali Liabes de Sidi Bel Abbes, Algeria
3Laboratory of Mathematics, University of Sidi Bel-Abbes, Sidi Bel-Abbes, Algeria
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 1, pp. 51-66 
J. R. Graef; H. Kadari; A. Ouahab; A. Oumansour; J. R. Graef; H. Kadari; A. Ouahab; A. Oumansour. Existence results for systems of second-order impulsive differential equations. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 1, pp. 51-66. http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a4/
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     author = {J. R. Graef and H. Kadari and A. Ouahab and A. Oumansour and J. R. Graef and H. Kadari and A. Ouahab and A. Oumansour},
     title = { Existence results for systems of second-order impulsive differential equations},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {51--66},
     year = {2019},
     volume = {88},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_1_a4/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper the authors study the existence of solutions to systems of nonlinear second order impulsive differential equations. Their results are established by using vector versions of Perov’s fixed point theorem and the nonlinear alternative of Leray-Schauder type. Both approaches are combined with a technique based on vector-valued metrics and matrices that converge to zero. Examples illustrating the results are included.