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

2021 ◽  
Vol 40 (1) ◽  
pp. 175-186
Author(s):  
Kuo-Shou Chiu
Keyword(s):  
Differential Equations ◽  
Monotone Iterative Technique ◽  
Iterative Technique ◽  
Constant Delay ◽  
Piecewise Constant ◽  
First Order ◽  
Monotone Iterative ◽  
Minimal And Maximal Solutions ◽  
Generalized Type ◽  
First Order Differential Equations

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).

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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