Nonoscillation and oscillation of second-order impulsive differential equations with periodic coefficients

Date

2012-03-01

Author

ÖZBEKLER, ABDULLAH
Zafer, Ağacık

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

318
views

0
downloads

In this paper, we give a nonoscillation criterion for half-linear equations with periodic coefficients under fixed moments of impulse actions. The method is based on the existence of positive solutions of the related Riccati equation and a recently obtained comparison principle. In the special case when the equation becomes impulsive Hill equation new oscillation criteria are also obtained.

Subject Keywords

Oscillation, Impulse, Half-linear, Periodic

URI

https://hdl.handle.net/11511/57865

Journal

APPLIED MATHEMATICS LETTERS

DOI

https://doi.org/10.1016/j.aml.2011.09.001

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Forced Oscillation of Second-Order Impulsive Differential Equations with Mixed Nonlinearities ÖZBEKLER, ABDULLAH; Zafer, Ağacık (2011-07-08) In this paper we give new oscillation criteria for a class of second-order mixed nonlinear impulsive differential equations having fixed moments of impulse actions. The method is based on the existence of a nonprincipal solution of a related second-order linear homogeneous equation.
SECOND ORDER OSCILLATION OF MIXED NONLINEAR DYNAMIC EQUATIONS WITH SEVERAL POSITIVE AND NEGATIVE COEFFICIENTS ÖZBEKLER, ABDULLAH; Zafer, Ağacık (2011-09-01) New oscillation criteria are obtained for superlinear and sublinear forced dynamic equations having positive and negative coefficients by means of nonprincipal solutions.
Stability criteria for linear periodic impulsive Hamiltonian systems Guseinov, G. Sh.; Zafer, Ağacık (2007-11-15) In this paper we obtain stability criteria for linear periodic impulsive Hamiltonian systems. A Lyapunov type inequality is established. Our results improve also the ones previously obtained for systems without impulse effect. (c) 2007 Elsevier Inc. All rights reserved.
PICONE TYPE FORMULA FOR NON-SELFADJOINT IMPULSIVE DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS SOLUTIONS ÖZBEKLER, ABDULLAH; Zafer, Ağacık (2010-01-01) A Picone type formula for second order linear non-selfadjoint impulsive differential equations with discontinuous solutions having fixed moments of impulse actions is derived. Applying the formula, Leighton and Sturm-Picone type comparison theorems as well as several oscillation criteria for impulsive differential equations are obtained.
Nonautonomous Bifurcations in Nonlinear Impulsive Systems Akhmet, Marat (Springer Science and Business Media LLC, 2020-01-01) In this paper, we study existence of the bounded solutions and asymptotic behavior of an impulsive Bernoulli equations. Nonautonomous pitchfork and transcritical bifurcation scenarios are investigated. An examples with numerical simulations are given to illustrate our results.

Citation Formats

A. ÖZBEKLER and A. Zafer, “Nonoscillation and oscillation of second-order impulsive differential equations with periodic coefficients,” APPLIED MATHEMATICS LETTERS, pp. 294–300, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57865.