Existence results for systems with nonlinear coupled nonlocal initial conditions

Octavia Bolojan; Gennaro Infante; Radu Precup

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 4, page 371-384
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Bolojan, Octavia, Infante, Gennaro, and Precup, Radu. "Existence results for systems with nonlinear coupled nonlocal initial conditions." Mathematica Bohemica 140.4 (2015): 371-384. <http://eudml.org/doc/271839>.

@article{Bolojan2015,
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.},
author = {Bolojan, Octavia, Infante, Gennaro, Precup, Radu},
journal = {Mathematica Bohemica},
keywords = {nonlinear differential system; nonlocal boundary condition; nonlinear boundary condition; fixed point; vector-valued norm; matrix convergent to zero},
language = {eng},
number = {4},
pages = {371-384},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Existence results for systems with nonlinear coupled nonlocal initial conditions},
url = {http://eudml.org/doc/271839},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Bolojan, Octavia
AU - Infante, Gennaro
AU - Precup, Radu
TI - Existence results for systems with nonlinear coupled nonlocal initial conditions
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 4
SP - 371
EP - 384
AB - 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.
LA - eng
KW - nonlinear differential system; nonlocal boundary condition; nonlinear boundary condition; fixed point; vector-valued norm; matrix convergent to zero
UR - http://eudml.org/doc/271839
ER -

References

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