Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Comparison Theorems for Even Order Dynamic Equations on Time Scales(Dynamic Publishers, inc, 2014) Jia Baoguo; Mert, Raziye; Erbe, Lynn; Mert, Raziye; MatematikConsider 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.Article On the Oscillation of Solutions of a Nonlinear Dynamic System on Time Scales(2012) Erbe, L.; Mert, Raziye; Mert, R.; MatematikWe 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.Article Citation - WoS: 2Citation - Scopus: 7A 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; MatematikTime 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.Article 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, RaziyeSome 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.Article Citation - WoS: 15Citation - Scopus: 15Spectral Parameter Power Series for Sturm-Liouville Equations on Time Scales(Elsevier Science inc, 2012) Mert, Raziye; Peterson, Allan; Erbe, LynnWe 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.