Open Access"Monotone iteration method for general nonlinear two point boundary value problems with deviating arguments"
Author(s) -
BAPURAO C. DHAGE,
JANHAVI B. DHAGE,
JAVID ALI
Publication year - 2022
Publication title -
carpathian journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.812
H-Index - 25
eISSN - 1843-4401
pISSN - 1584-2851
DOI - 10.37193/cjm.2022.02.11
Subject(s) - mathematics , monotone polygon , boundary value problem , nonlinear system , banach space , mathematical analysis , dirichlet distribution , ordinary differential equation , differential equation , fixed point theorem , dirichlet boundary condition , physics , geometry , quantum mechanics
"In this paper we shall study the existence and approximation results for a nonlinear two point boundary value problem of a second order ordinary differential equation with general form of Dirichlet/Neumann type boundary conditions. The nonlinearity present on right hand side of the differential equation is assumed to be Caratho´eodory containing a deviating argument. The proofs of the main results are based on a monotone iteration method contained in the hybrid fixed point principles of Dhage (2014) in an ordered Banach space. Finally, some remarks concerning the merits of our monotone iteration method over other frequently used iteration methods in the theory of nonlinear differential equations are given in the conclusion."