Geodesic
Initial-value problems for first-order differential systems with general nonlocal conditions
Electronic journal of differential equations, Tome 2012 (2012)
This article concerns the existence of solutions to initial-value problems for nonlinear first-order differential systems with nonlocal conditions of functional type. The fixed point principles by Perov, Schauder and Leray-Schauder are applied to a nonlinear integral operator split into two operators, one of Fredholm type and the other of Volterra type. The novelty in this article is combining this approach with the technique that uses convergent to zero matrices and vector norms.
Classification : 34A34, 34A12, 45G10
Keywords: nonlinear differential system, nonlocal initial condition, fixed point, vector norm, matrix convergent to zero 
@article{EJDE_2012__2012__a55,
     author = {Nica,  Octavia},
     title = {Initial-value problems for first-order differential systems with general nonlocal conditions},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1261.34016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a55/}
}
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JO  - Electronic journal of differential equations
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VL  - 2012
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%A Nica,  Octavia
%T Initial-value problems for first-order differential systems with general nonlocal conditions
%J Electronic journal of differential equations
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%V 2012
%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a55/
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%F EJDE_2012__2012__a55
Nica,  Octavia. Initial-value problems for first-order differential systems with general nonlocal conditions. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a55/