Browsing by Author "Mert, Raziye"

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Comparison Theorems for Even Order Dynamic Equations on Time Scales
(Dynamic Publishers, inc, 2014) Jia Baoguo; Mert, Raziye; Erbe, Lynn; Mert, Raziye; Matematik
Consider the following pair of even order linear dynamic equations on a time scale (0.1) x(Delta n)(t) + p(t)x(t) = 0, (0.2) x(Delta n)(t) + q(t)x(t) = 0, where p, q is an element of C-rd(T,R+), n is even, T is a time scale. In this paper, we obtain some point-wise and integral comparison theorems for the above equations. These will be shown to be "sharp" by means of specific examples.
Citation - WoS: 5
Citation - Scopus: 5
A Halanay-Type Inequality on Time Scales in Higher Dimensional Spaces
(Element, 2014) Erbe, Lynn; Mert, Raziye; Jia, Baoguo
In this paper, we investigate a certain class of Halanay-type inequalities on time scales in higher dimensional spaces. By means of the obtained inequality, we derive some new global stability conditions for linear delay dynamic systems on time scales. An example is given to illustrate the results.
Citation - WoS: 2
Citation - Scopus: 7
A Necessary and Sufficient Condition for Oscillation of Second Order Sublinear Delay Dynamic Equations
(Amer inst Mathematical Sciences-aims, 2011) Mert, RazIye; Mert, Raziye; Zafer, Agacik; Matematik
Time scale calculus approach allows one to treat the continuous, discrete, as well as more general systems simultaneously. In this article we use this tool to establish a necessary and sufficient condition for the oscillation of a class of second order sublinear delay dynamic equations on time scales. Some well known results in the literature are improved and extended.
On the Oscillation of Solutions of a Nonlinear Dynamic System on Time Scales
(2012) Erbe, L.; Mert, Raziye; Mert, R.; Matematik
We study the oscillation properties of a system of two first-order nonlinear equations on time scales. This form includes the classical Emden-Fowler differential and difference equations and many of its extensions. We provide a corrected formulation of some earlier oscillation results as well as providing some new oscillation criteria. © Dynamic Publishers, Inc.
Oscillation criteria for even order dynamic equations on time-scales
(Dynamic Publishers, Inc, 2011) Grace, Said R.; Agarwal, Ravi P.; Kaymakçalan, Billur; Baoguo, Jia; Erbe, Lynn; Mert, Raziye
Some new criteria for the oscillation of even order linear dynamic equations on time-scales of the form xΔn(t) + q(t)x(t) = 0 are established.
Citation - WoS: 14
Citation - Scopus: 18
Oscillation of Even Order Nonlinear Delay Dynamic Equations on Time Scales
(Springer Heidelberg, 2013) Mert, Raziye; Peterson, Allan; Zafer, Agacik; Erbe, Lynn
One of the important methods for studying the oscillation of higher order differential equations is to make a comparison with second order differential equations. The method involves using Taylor's Formula. In this paper we show how such a method can be used for a class of even order delay dynamic equations on time scales via comparison with second order dynamic inequalities. In particular, it is shown that nonexistence of an eventually positive solution of a certain second order delay dynamic inequality is sufficient for oscillation of even order dynamic equations on time scales. The arguments are based on Taylor monomials on time scales.
Citation - WoS: 7
Citation - Scopus: 10
Oscillation of Higher-Order Neutral Dynamic Equations on Time Scales
(Springeropen, 2012) Mert, Raziye
In this article, using comparison with second-order dynamic equations, we establish sufficient conditions for oscillatory solutions of an nth-order neutral dynamic equation with distributed deviating arguments. The arguments are based on Taylor monomials on time scales. 2000 Mathematics Subject Classification: 34K11; 39A10; 39A99.
Citation - WoS: 8
Citation - Scopus: 5
Oscillatory Behavior of Higher-Order Neutral Type Dynamic Equations
(Univ Szeged, Bolyai institute, 2013) Mert, Raziye; Zafer, Agacik; Grace, Said R.
The oscillation behavior of solutions for higher-order delay dynamic equations of neutral type is investigated by making use of comparison with second-order dynamice quations. The method can be utilized to study other types of higher-order equations on time scales as well.
Citation - WoS: 15
Citation - Scopus: 15
Spectral Parameter Power Series for Sturm-Liouville Equations on Time Scales
(Elsevier Science inc, 2012) Mert, Raziye; Peterson, Allan; Erbe, Lynn
We will derive formulas for finding two linearly independent solutions of the Sturm-Liouville dynamic equation. We will give several examples. In particular, the q-difference equation which has important applications in quantum theory will be presented. (C) 2012 Elsevier Inc. All rights reserved.