Existence results for systems with coupled nonlocal conditions


In this paper an existence theory is developed for first-order differential systems with coupled nonlocal conditions given by Stieltjes integrals. The approach is based on the fixed point theorems of Perov, Schauder and Schaefer and on a vector method for treating systems which uses matrices having spectral radius less than one. When the nonlocal conditions depend on functionals restricted to a proper subinterval, the nonlinear integral operator associated to the system splits into two parts, one of Fredholm type and another one of Volterra type. Correspondingly, the sufficient conditions for the existence results will differ in the two parts of the interval. Some examples are presented to illustrate the theory.


Octavia Bolojan-Nica
Departamentul de Matematică, Universitatea Babeş-Bolyai, Cluj 400084, Romania

Gennaro Infante
Dipartimento di Matematica ed Informatica, Università della Calabria, 87036 Arcavacata di Rende, Cosenza, Italy

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Nonlinear differential system; Nonlocal condition; Fixed point; Vector-valued norm; Inverse-positive matrix

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O. Bolojan-Nica, G. Infante, R. Precup, Existence results for systems with coupled nonlocal conditions, Nonlinear Anal. 94 (2014), 231-242, https://doi.org/10.1016/j.na.2013.08.019



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Nonlinear Analysis: Theory, Methods & Applications

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Elsevier Ltd

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