Monotone iterative technique for the initial value problem for differential equations with non-instantaneous impulses

2017 ◽  
Vol 298 ◽  
pp. 45-56 ◽  
Author(s):  
Ravi Agarwal ◽  
D. O'Regan ◽  
S. Hristova
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Initial Value ◽  
Monotone Iterative

scholarly journals Initial Value Problem For Nonlinear Fractional Differential Equations With ψ-Caputo Derivative Via Monotone Iterative Technique

Axioms ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 57 ◽  
Author(s):  
Choukri Derbazi ◽  
Zidane Baitiche ◽  
Mouffak Benchohra ◽  
Alberto Cabada
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Value Problem ◽  
Caputo Derivative ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Initial Value ◽  
Monotone Iterative ◽  
Fractional Differential

In this article, we discuss the existence and uniqueness of extremal solutions for nonlinear initial value problems of fractional differential equations involving the ψ -Caputo derivative. Moreover, some uniqueness results are obtained. Our results rely on the standard tools of functional analysis. More precisely we apply the monotone iterative technique combined with the method of upper and lower solutions to establish sufficient conditions for existence as well as the uniqueness of extremal solutions to the initial value problem. An illustrative example is presented to point out the applicability of our main results.

scholarly journals Application of Lakshmikantham's monotone-iterative technique to the solution of the initial value problem for impulsive integro-differential equations

1993 ◽  
Vol 6 (1) ◽  
pp. 25-34 ◽  
Author(s):  
D. D. Bainov ◽  
S. G. Hristova
Keyword(s):  
Differential Equations ◽  
Initial Value Problem ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Initial Value ◽  
Volterra Type ◽  
Monotone Iterative

In the present paper, a technique of V. Lakshmikantham is applied to approximate finding of extremal quasisolutions of an initial value problem for a system of impulsive integro-differential equations of Volterra type.

scholarly journals Monotone-iterative technique of Lakshmikantham for the initial value problem for a differential equation with a step function

2002 ◽  
Vol 30 (1) ◽  
pp. 57-62
Author(s):  
S. G. Hristova ◽  
M. A. Rangelova
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Initial Value Problem ◽  
Special Kind ◽  
Step Function ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Initial Value ◽  
Monotone Iterative ◽  
The Given

The initial value problem for a special kind of differential equations with a step function is studied. The monotone-iterative technique of Lakshmikantham for approximate finding of the solutions of the given problem is well grounded.

Ordinary Differential Equations with Nonlinear Boundary Conditions

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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