Geodesic
Existence results for systems with nonlinear coupled nonlocal initial conditions
Mathematica Bohemica, Tome 140 (2015) no. 4, pp. 371-384.

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The purpose of the present paper is to study the existence of solutions to initial value problems for nonlinear first order differential systems subject to nonlinear nonlocal initial conditions of functional type. The approach uses vector-valued metrics and matrices convergent to zero. Two existence results are given by means of Schauder and Leray-Schauder fixed point principles and the existence and uniqueness of the solution is obtained via a fixed point theorem due to Perov. Two examples are given to illustrate the theory.
DOI : 10.21136/MB.2015.144455
Classification : 34A12, 34A34, 34B10, 47H10
Keywords: nonlinear differential system; nonlocal boundary condition; nonlinear boundary condition; fixed point; vector-valued norm; matrix convergent to zero 
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Bolojan, Octavia; Infante, Gennaro; Precup, Radu. Existence results for systems with nonlinear coupled nonlocal initial conditions. Mathematica Bohemica, Tome 140 (2015) no. 4, pp. 371-384. doi : 10.21136/MB.2015.144455. http://geodesic.mathdoc.fr/articles/10.21136/MB.2015.144455/

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