Monotone iterative technique for impulsive differential equations with time variables

2000 ◽  
Vol 7 (2) ◽  
pp. 419-432
Author(s):  
Jiangang Qi ◽  
Yansheng Liu
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Monotone Iterative ◽  
Time Variables

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.

Monotone iterative method for a class of nonlinear fractional differential equations

2012 ◽  
Vol 15 (2) ◽  
Author(s):  
Guotao Wang ◽  
Dumitru Baleanu ◽  
Lihong Zhang
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Fractional Differential Equations ◽  
Monotone Iterative Technique ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Nonlinear Fractional Differential Equations ◽  
Monotone Iterative ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

AbstractBy applying the monotone iterative technique and the method of lower and upper solutions, this paper investigates the existence of extremal solutions for a class of nonlinear fractional differential equations, which involve the Riemann-Liouville fractional derivative D q x(t). A new comparison theorem is also build. At last, an example is given to illustrate our main results.

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

1997 ◽  
Vol 10 (1) ◽  
pp. 71-78 ◽  
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.

scholarly journals Periodic problem for non-instantaneous impulsive partial differential equations

2021 ◽  
Vol 7 (3) ◽  
pp. 3345-3359
Author(s):  
Huanhuan Zhang ◽  
◽  
Jia Mu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mild Solutions ◽  
Periodic Problem ◽  
Lower Solution ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Partial Differential ◽  
Monotone Iterative ◽  
Impulsive Equation

<abstract><p>We obtain a new maximum principle of the periodic solutions when the corresponding impulsive equation is linear. If the nonlinear is quasi-monotonicity, we study the existence of the minimal and maximal periodic mild solutions for impulsive partial differential equations by using the perturbation method, the monotone iterative technique and the method of upper and lower solution. We give an example in last part to illustrate the main theorem.</p></abstract>

scholarly journals Monotone Iterative Technique for Conformable Fractional Differential Equations with Deviating Arguments

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Huiling Chen ◽  
Shuman Meng ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Iterative Technique ◽  
Deviating Arguments ◽  
Comparison Principles ◽  
Monotone Iterative ◽  
Fractional Differential

This paper is concerned with the existence of extremal solutions for periodic boundary value problems for conformable fractional differential equations with deviating arguments. We first build two comparison principles for the corresponding linear equation with deviating arguments. With the help of new comparison principles, some sufficient conditions for the existence of extremal solutions are established by combining the method of lower and upper solutions and the monotone iterative technique. As an application, an example is presented to enrich the main results of this article.

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