Solution of Hallam's Problem on the Terminal Comparison Principle for Ordinary Differential Inequalities

1976 ◽  
Vol 220 ◽  
pp. 115
Author(s):  
Giovanni Vidossich
Keyword(s):  
Comparison Principle ◽  
Differential Inequalities

GUARANTEED STRATEGIES FOR NONLINEAR MULTI-PLAYER PURSUIT-EVASION GAMES

2010 ◽  
Vol 12 (01) ◽  
pp. 1-17 ◽  
Author(s):  
DUŠAN M. STIPANOVIĆ ◽  
ARIK MELIKYAN ◽  
NAIRA HOVAKIMYAN
Keyword(s):  
Comparison Principle ◽  
Nonlinear Dynamic ◽  
Arbitrary Number ◽  
Dynamic Models ◽  
Differential Inequalities ◽  
Design Strategies ◽  
Maximum Function ◽  
Pursuit Evasion ◽  
Nonlinear Dynamic Models

In this paper, we provide a methodology to design strategies for either guaranteed capture or guaranteed evasion in the case of pursuit-evasion games with multiple players which are represented by nonlinear dynamic models. This methodology is based on the continuously differentiable upper and lower approximations of the minimum and maximum function of an arbitrary number of arguments, comparison principle, and differential inequalities.

Differential inequalities and extension of Lyapunov's method

1964 ◽  
Vol 60 (4) ◽  
pp. 891-895 ◽  
Author(s):  
V. Lakshmikantham
Keyword(s):  
Differential Equations ◽  
Comparison Principle ◽  
Direct Method ◽  
Linear Differential Equations ◽  
Maximal Solution ◽  
Differential Inequalities ◽  
Non Linear ◽  
Linear Differential ◽  
Lyapunov’S Method ◽  
Image Position

One of the most important techniques in the theory of non-linear differential equations is the direct method of Lyapunov and its extensions. It depends basically on the fact that a function satisfying the inequalityis majorized by the maximal solution of the equationUsing this comparison principle and the concept of Lyapunov's function various properties of solutions of differential equations have been considered (1–11).

Existence on solutions of a class of casual differential equations on a time scale

2021 ◽  
Vol 71 (3) ◽  
pp. 683-696
Author(s):  
Yige Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Algebra ◽  
Existence Theorem ◽  
Point Theorem ◽  
Comparison Principle ◽  
Time Scale ◽  
Differential Inequalities ◽  
The Fixed Point Theorem

Abstract In this paper, we develop the theory of a class of casual differential equations on a time scale. An existence theorem for casual differential equations on a time scale is given under mixed Lipschitz and compactness conditions by the fixed point theorem in Banach algebra due to Dhage. Some fundamental differential inequalities on a time scale are also presented which are utilized to investigate the existence of extremal solutions. The comparison principle on casual differential equations on a time scale is established. Our results in this paper extend and improve some well-known results.

scholarly journals Second method of Lyapunov and comparison principle for impulsive differential–difference equations

1997 ◽  
Vol 38 (4) ◽  
pp. 489-505 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Comparison Principle ◽  
Difference Equations ◽  
Continuous Functions ◽  
Differential Inequalities ◽  
Impulse Effect ◽  
Comparison Equation ◽  
Piecewise Continuous ◽  
Second Method Of Lyapunov

AbstractIn the present paper questions related to stability and boundedness with respect to manifolds of solutions of impulsive differential-difference equations are considered. The investigations are carried out by means of piecewise-continuous functions which are analogues of the classical Lyapunov's functions. By means of a vectorial comparison equation and differential inequalities for piecewise-continuous functions, theorems are proved on stability and boundedness with respect to manifolds of solutions of impulsive differential-difference equations with impulse effect at fixed moments.

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