MATHEMATICA BOHEMICA, Vol. 140, No. 4, pp. 371-384, 2015

Existence results for systems with nonlinear coupled nonlocal initial conditions

Octavia Bolojan, Gennaro Infante, Radu Precup

Octavia Bolojan-Nica, Universitatea Babeş-Bolyai, Departamentul de Matematică, Mihail Kogălnicenu 1, Cluj-Napoca, 400 084 România, e-mail: octavia.nica@math.ubbcluj.ro; Gennaro Infante, Universita della Calabria, Dipartimento di Matematica ed Informatica, 870 36 Arcavacata di Rende, Cosenza, Italy, e-mail: gennaro.infante@unical.it; Radu Precup, Universitatea Babeş-Bolyai, Departamentul de Matematică, Mihail Kogălnicenu 1, Cluj-Napoca, 400 084 Romania, e-mail: r.precup@math.ubbcluj.ro

Abstract: 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.

Keywords: nonlinear differential system; nonlocal boundary condition; nonlinear boundary condition; fixed point; vector-valued norm; matrix convergent to zero

Classification (MSC 2010): 34A34, 34A12, 34B10, 47H10


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