Minimal and maximal solutions to first-order differential equations with piecewise constant generalized delay

In this paper we employ the method of maximal and minimal solutions coupled with comparison principles and the monotone iterative technique to obtain results of existence and approximation of solutions for differential equations with piecewise constant delay of generalized type (DEPCAG).

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Monotone iterative technique for a coupled system of first order differential equations

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics ◽

10.1501/commua1_0000000693 ◽

2013 ◽

Vol 62 (2) ◽

pp. 1-11

Author(s):

DEMİRCİ Elif; ÖZALP

Keyword(s):

Differential Equations ◽

Coupled System ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

First Order ◽

Monotone Iterative ◽

First Order Differential Equations

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Systems of First Order Partial Differential Equations and Monotone Iterative Technique

Trends in The Theory and Practice of Non-Linear Analysis, Proceedings of the VIth International Conference on Trends in the Theory and Practice of Non-Linear Analysis - North-Holland Mathematics Studies ◽

10.1016/s0304-0208(08)72717-8 ◽

1985 ◽

pp. 249-255 ◽

Cited By ~ 1

Author(s):

G.S. Ladde ◽

A.S. Vatsala

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

Partial Differential ◽

First Order ◽

Monotone Iterative

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Monotone iterative technique for partial differential equations of first order

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(84)90179-3 ◽

1984 ◽

Vol 102 (2) ◽

pp. 393-398 ◽

Cited By ~ 7

Author(s):

V Lakshmikantham ◽

M.N Oguztöreli ◽

A.S Vatsala

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

Partial Differential ◽

First Order ◽

Monotone Iterative

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Terminal value problems of impulsive integro-differential equations in Banach spaces

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953397000075 ◽

1997 ◽

Vol 10 (1) ◽

pp. 71-78 ◽

Cited By ~ 4

Author(s):

Dajun Guo

Keyword(s):

Banach Space ◽

Differential Equations ◽

Banach Spaces ◽

Mixed Type ◽

Monotone Iterative Technique ◽

Iterative Technique ◽

First Order ◽

Monotone Iterative ◽

Equations Of Mixed Type ◽

Nonnegative Solutions

This paper uses cone theory and the monotone iterative technique to investigate the existence of minimal nonnegative solutions of terminal value problems for first order nonlinear impulsive integro-differential equations of mixed type in a Banach space.

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OSCILLATORY AND ASYMPTOTIC PROPERTIES OF NONLINEAR FIRST ORDER DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT OF GENERALIZED TYPE

International Journal of Pure and Apllied Mathematics ◽

10.12732/ijpam.v110i3.13 ◽

2016 ◽

Vol 110 (3) ◽

Author(s):

T. Kostadinov ◽

V. Proycheva

Keyword(s):

Differential Equations ◽

Asymptotic Properties ◽

Piecewise Constant ◽

First Order ◽

Piecewise Constant Argument ◽

Generalized Type ◽

First Order Differential Equations ◽

Constant Argument

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The Monotone Iterative Technique and Periodic Boundary Value Problem for First Order Impulsive Functional Differential Equations

Acta Mathematica Sinica English Series ◽

10.1007/s101140200155 ◽

2002 ◽

Vol 18 (2) ◽

pp. 253-262 ◽

Cited By ~ 2

Author(s):

Zhi Min He ◽

Wei Gao Ge

Keyword(s):

Differential Equations ◽

Boundary Value Problem ◽

Periodic Boundary ◽

Functional Differential Equations ◽

Monotone Iterative Technique ◽

Periodic Boundary Value Problem ◽

Iterative Technique ◽

First Order ◽

Monotone Iterative ◽

Functional Differential

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A generalized upper and lower solutions method for nonlinear second order ordinary differential equations

Journal of Applied Mathematics and Stochastic Analysis ◽

10.1155/s1048953392000133 ◽

1992 ◽

Vol 5 (2) ◽

pp. 157-165 ◽

Cited By ~ 6

Author(s):

Juan J. Nieto ◽

Alberto Cabada

Keyword(s):

Differential Equations ◽

Boundary Value Problem ◽

Nonlinear Boundary ◽

Upper And Lower Solutions ◽

Monotone Iterative Technique ◽

Second Order ◽

Iterative Technique ◽

Monotone Iterative ◽

Carathéodory Function ◽

Minimal And Maximal Solutions

The purpose of this paper is to study a nonlinear boundary value problem of second order when the nonlinearity is a Carathéodory function. It is shown that a generalized upper and lower solutions method is valid, and the monotone iterative technique for finding the minimal and maximal solutions is developed.

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Minimal and maximal solutions to systems of differential equations with a singular matrix

The ANZIAM Journal ◽

10.1017/s1446181100013286 ◽

2003 ◽

Vol 45 (2) ◽

pp. 223-231

Author(s):

Tadeusz Jankowski

Keyword(s):

Differential Equations ◽

Ordinary Differential Equations ◽

Monotone Iterative Technique ◽

Extremal Solutions ◽

Iterative Technique ◽

Singular Matrix ◽

Monotone Iterative ◽

Maximal Solutions ◽

Systems Of Differential Equations ◽

Minimal And Maximal Solutions

AbstractThe monotone iterative technique is applied to a system of ordinary differential equations with a singular matrix. The existence of extremal solutions is proved.

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Ordinary Differential Equations with Nonlinear Boundary Conditions

Georgian Mathematical Journal ◽

10.1515/gmj.2002.287 ◽

2002 ◽

Vol 9 (2) ◽

pp. 287-294

Author(s):

Tadeusz Jankowski

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Ordinary Differential Equations ◽

Nonlinear Boundary ◽

Nonlinear Boundary Conditions ◽

Existence Results ◽

Monotone Iterative Technique ◽

Lower And Upper Solutions ◽

Iterative Technique ◽

Monotone Iterative

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.

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