Monotone-iterative method for solving the periodic problem for systems of impulsive differential equations

1988 ◽  
Vol 27 (6) ◽  
pp. 757-766 ◽  
Author(s):  
S. G. Hristova ◽  
D. D. Bainov
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Impulsive Differential Equations ◽  
Periodic Problem ◽  
Monotone Iterative Method ◽  
Monotone Iterative

scholarly journals A monotone iterative method for boundary value problems of parametric differential equations

2001 ◽  
Vol 14 (2) ◽  
pp. 183-187 ◽  
Author(s):  
Xinzhi Liu ◽  
Farzana A. McRae
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Monotone Sequences

This paper studies boundary value problems for parametric differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and proved to converge to the extremal solutions of the boundary value problem.

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 Monotone iterative method for fractional p-Laplacian differential equations with four-point boundary conditions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaoping Li ◽  
Minyuan He
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Iterative Method ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Positive Solutions ◽  
Monotone Iterative Method ◽  
Point Boundary ◽  
Abstract Result ◽  
Monotone Iterative

AbstractA four-point boundary problem for a fractional p-Laplacian differential equation is studied. The existence of two positive solutions is established by means of the monotone iterative method. An example supporting the abstract result is given.

A MONOTONE-ITERATIVE METHOD FOR FINDING PERIODIC SOLUTION OF AN IMPULSIVE DIFFERENTIAL EQUATIONS AND APPLICATION

2008 ◽  
Vol 01 (02) ◽  
pp. 247-256
Author(s):  
JIAWEI DOU
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Upper And Lower Solutions ◽  
Impulsive Differential Equations ◽  
Iteration Process ◽  
Impulsive System ◽  
Monotone Iterative Method ◽  
Initial Value ◽  
Monotone Iterative ◽  
Monotone Iterations

In this paper, using the method of upper and lower solutions and its associated monotone iterations, we establish a new monotone-iterative scheme for finding periodic solutions of an impulsive differential equations. This method leads to the existence of maximal and minimal periodic solutions which can be computed from a linear iteration process in the same fashion as for impulsive differential equations initial value problem. This method is constructive and can be used to develop a computational algorithm for numerical solution of the periodic impulsive system. Our existence result improves a result established in [1]. The result is applied to a model of mutualism of Lotka–Volterra type which involves interactions among a mutualist-competitor, a competitor and a mutualist, the existence of positive periodic solutions of the model is obtained.

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