scholarly journals Variational analysis to fourth-order impulsive differential equations

2018 ◽  
Vol 38 (1) ◽  
pp. 151-163
Author(s):  
Saeid Shokooh
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Critical Point ◽  
Fourth Order ◽  
Variational Analysis ◽  
Impulsive Differential Equation ◽  
Impulsive Differential Equations ◽  
Three Solutions ◽  
One Dimensional ◽  
Critical Point Theorems

Applying two critical point theorems, we prove the existence of atleast three solutions for a one-dimensional fourth-order impulsive differential equation with two real parameters.

scholarly journals Bifurcation of Bounded Solutions of Impulsive Differential Equations

2016 ◽  
Vol 26 (14) ◽  
pp. 1650242 ◽  
Author(s):  
Kevin E. M. Church ◽  
Xinzhi Liu
Keyword(s):  
Differential Equation ◽  
Integral Operator ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Necessary Condition ◽  
Bounded Solutions ◽  
Pitchfork Bifurcations ◽  
Nonlinear Integral Operator

In this article, we examine nonautonomous bifurcation patterns in nonlinear systems of impulsive differential equations. The approach is based on Lyapunov–Schmidt reduction applied to the linearization of a particular nonlinear integral operator whose zeroes coincide with bounded solutions of the impulsive differential equation in question. This leads to sufficient conditions for the presence of fold, transcritical and pitchfork bifurcations. Additionally, we provide a computable necessary condition for bifurcation in nonlinear scalar impulsive differential equations. Several examples are provided illustrating the results.

scholarly journals Lp-equivalence of a linear and a nonlinear impulsive differential equation in a Banach space

1993 ◽  
Vol 36 (1) ◽  
pp. 17-33 ◽  
Author(s):  
D. D. Bainov ◽  
S. I. Kostadinov ◽  
P. P. Zabreiko
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations

In the present paper by means of the Schauder-Tychonoff principle sufficient conditions are obtained for Lp-equivalence of a linear and a nonlinear impulsive differential equations.

scholarly journals Sufficient conditions for oscillations of all solutions of a class of impulsive differential equations with deviating argument

1996 ◽  
Vol 9 (1) ◽  
pp. 33-42 ◽  
Author(s):  
D. D. Bainov ◽  
M. B. Dimitrova
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Deviating Argument ◽  
All Solutions

Sufficient conditions are found for oscillation of all solutions of impulsive differential equation with deviating argument.

scholarly journals Existence and Uniqueness of Mild Solutions for Nonlinear Stochastic Impulsive Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
L. J. Shen ◽  
J. T. Sun
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Stochastic Analysis ◽  
Impulsive Differential Equation ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Analysis Technique

This paper investigates the existence and uniqueness of mild solutions to the general nonlinear stochastic impulsive differential equations. By using Schaefer's fixed theorem and stochastic analysis technique, we propose sufficient conditions on existence and uniqueness of solution for stochastic differential equations with impulses. An example is also discussed to illustrate the effectiveness of the obtained results.

Oscillatory Properties of Solutions of Impulsive Differential Equations with Several Retarded Arguments

1998 ◽  
Vol 5 (3) ◽  
pp. 201-212
Author(s):  
D. D. Bainov ◽  
M. B. Dimitrova ◽  
V. A. Petrov
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Impulsive Differential Equation ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
All Solutions ◽  
Oscillatory Properties

Abstract The impulsive differential equation with several retarded arguments is considered, where pi (t) ≥ 0, 1 + bk > 0 for i = 1, . . . , m, t ≥ 0, k ∈ ℕ. Sufficient conditions for the oscillation of all solutions of this equation are found.

Infinitely many solutions for a class of fourth-order impulsive differential equations

2019 ◽  
Vol 10 (1) ◽  
pp. 7-16
Author(s):  
Saeid Shokooh ◽  
Ghasem A. Afrouzi
Keyword(s):  
Differential Equations ◽  
Critical Point ◽  
Point Theorem ◽  
Fourth Order ◽  
Impulsive Differential Equations ◽  
Infinitely Many Solutions ◽  
Critical Point Theorem

AbstractIn this paper, by employing a critical point theorem, we establish the existence of infinitely many solutions for fourth-order impulsive differential equations depending on two real parameters.

CONTINUOUS DEPENDENCE ON A PARAMETER OF THE SOLUTIONS OF IMPULSIVE DIFFERENTIAL EQUATIONS IN A BANACH SPACE

1993 ◽  
Vol 03 (04) ◽  
pp. 477-483
Author(s):  
D.D. BAINOV ◽  
S.I. KOSTADINOV ◽  
NGUYEN VAN MINH ◽  
P.P. ZABREIKO
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Equations ◽  
Small Parameter ◽  
Continuous Dependence ◽  
Impulsive Differential Equation ◽  
Impulsive Differential Equations ◽  
Right Hand ◽  
Dependence On A Parameter ◽  
The Right

Continuous dependence of the solutions of an impulsive differential equation on a small parameter is proved under the assumption that the right-hand side of the equation and the impulse operators satisfy conditions of Lipschitz type.

scholarly journals On the existence of solutions of one-dimensional fourth-order equations

2020 ◽  
Vol 72 (11) ◽  
pp. 1575-1588
Author(s):  
S. Shokooh ◽  
G. A. Afrouzi ◽  
A. Hadjian
Keyword(s):  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Existence Of Solutions ◽  
Nontrivial Solutions ◽  
Multiplicity Results ◽  
One Dimensional ◽  
Critical Point Theorems ◽  
Fourth Order Equations

UDC 517.9 Using variational methods and critical point theorems, we prove the existence of nontrivial solutions for one-dimensional fourth-order equations. Multiplicity results are also pointed out.

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