PICONE TYPE FORMULA FOR NON-SELFADJOINT IMPULSIVE DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS SOLUTIONS

Date

2010-01-01

Author

ÖZBEKLER, ABDULLAH
Zafer, Ağacık

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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.

Subject Keywords

Picone type formula, Sturm-Picone comparison, Leighton comparison, Oscillation, Second order, Non-selfadjoint, Impulse

URI

https://hdl.handle.net/11511/52698

Journal

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS

Collections

Department of Mathematics, Article

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Picone's formula for linear non-selfadjoint impulsive differential equations Ozbekler, A.; Zafer, Ağacık (Elsevier BV, 2006-07-15) In this paper, we derive a Picone type formula for second-order linear non-selfadjoint impulsive differential equations having fixed moments of impulse actions, and obtain a Wirtinger type inequality, a Leighton type comparison theorem, and a Sturm-Picone comparison theorem for such equations. Moreover, several oscillation criteria are also derived as applications. (c) 2005 Elsevier Inc. All rights reserved.
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.
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.
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.
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.

Citation Formats

A. ÖZBEKLER and A. Zafer, “PICONE TYPE FORMULA FOR NON-SELFADJOINT IMPULSIVE DIFFERENTIAL EQUATIONS WITH DISCONTINUOUS SOLUTIONS,” ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, pp. 1–12, 2010, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/52698.