On oscillation and nonoscillation of second-order dynamic equations

Zafer, Ağacık
New oscillation and nonoscillation criteria are established for second-order linear equations with damping and forcing terms. Examples are given to illustrate the results.


On Stability of Linear Delay Differential Equations under Perron's Condition
Diblík, J.; Zafer, A. (Hindawi Limited, 2011)
The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.
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.
Nonlinear oscillation of second-order dynamic equations on time scales
Anderson, Douglas R.; Zafer, Ağacık (Elsevier BV, 2009-10-01)
Interval oscillation criteria are established for a second-order nonlinear dynamic equation on time scales by utilizing a generalized Riccati technique and the Young inequality. The theory can be applied to second-order dynamic equations regardless of the choice of delta or nabla derivatives.
On the smoothness of solutions of impulsive autonomous systems
Akhmet, Marat (Elsevier BV, 2005-01-01)
The aim of this paper is to investigate dependence of solutions on parameters for nonlinear autonomous impulsive differential equations. We will specify what continuous, differentiable and analytic dependence of solutions on parameters is, define higher order derivatives of solutions with respect to parameters and determine conditions for existence of such derivatives. The theorem of analytic dependence of solutions on parameters is proved.
Global existence and boundedness for a class of second-order nonlinear differential equations
Tiryaki, Aydin; Zafer, Ağacık (Elsevier BV, 2013-09-01)
In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form
Citation Formats
A. Zafer, “On oscillation and nonoscillation of second-order dynamic equations,” APPLIED MATHEMATICS LETTERS, pp. 136–141, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/57353.