Forced Oscillation of Second-Order Impulsive Differential Equations with Mixed Nonlinearities

Date

2011-07-08

Author

ÖZBEKLER, ABDULLAH
Zafer, Ağacık

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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.

Subject Keywords

Oscillation, Mixed nonlinear, Fixed moments, Impulse, Non-principal

URI

https://hdl.handle.net/11511/57665

DOI

https://doi.org/10.1007/978-1-4614-7333-6_13

Conference Name

International Conference on Differential and Difference Equations and Applications

Collections

Department of Mathematics, Conference / Seminar

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Nonoscillation and oscillation of second-order impulsive differential equations with periodic coefficients ÖZBEKLER, ABDULLAH; Zafer, Ağacık (2012-03-01) 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.
Oscillation of second-order nonlinear differential equations with nonlinear damping Tiryaki, A; Zafer, Ağacık (2004-01-01) This paper is concerned with the oscillation of a class of general type second-order differential equations with nonlinear damping terms. Several new oscillation criteria are established for such a class of differential equations under quite general assumptions. Examples are also given to illustrate the results.
Forced oscillation of super-half-linear impulsive differential equations Oezbekler, A.; Zafer, Ağacık (Elsevier BV, 2007-09-01) By using a Picone type formula in comparison with oscillatory unforced half-linear equations, we derive new oscillation criteria for second order forced super-half-linear impulsive differential equations having fixed moments of impulse actions. In the superlinear case, the effect of a damping term is also considered.
Forced oscillation of second-order nonlinear differential equations with positive and negative coefficients ÖZBEKLER, ABDULLAH; Wong, J. S. W.; Zafer, Ağacık (Elsevier BV, 2011-07-01) In this paper we give new oscillation criteria for forced super- and sub-linear differential equations by means of nonprincipal solutions.
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.

Citation Formats

A. ÖZBEKLER and A. Zafer, “Forced Oscillation of Second-Order Impulsive Differential Equations with Mixed Nonlinearities,” Azores Univ, Ponta Delgada, PORTUGAL, 2011, vol. 47, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57665.