Browsing by Author "Erbe, Lynn"

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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; 19485; 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; 19485
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: 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; 19485
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: 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; 19485
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.