Open AccessExistence and uniqueness of solutions for the first-order non-linear differential equations with three-point boundary conditions
Author(s) -
Mısır J. Mardanov,
A Yagub Sharifov,
E Kamala Ismayilova
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1905387m
Subject(s) - mathematics , uniqueness , contraction principle , contraction mapping , boundary value problem , fixed point theorem , mathematical analysis , picard–lindelöf theorem , ordinary differential equation , order (exchange) , differential equation , finance , economics
In this paper the existence and uniqueness of the solutions to boundary value problems for the first order non-linear system of the ordinary differential equations with three-point boundary conditions are investigated. For the first time the Green function is constructed and the considered problem is reduced to the equivalent integral equations that allow us to prove the existence and uniqueness theorems in differ from existing works, applying the Banach contraction mapping principle and Schaefer?s fixed point theorem. An example is given to illustrate the obtained results.