Mert, Raziye
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Yrd. Doç. Dr.
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Matematik
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Former Staff
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Scholarly Output
11
Articles
22
Citation Count
67
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0
11 results
Scholarly Output Search Results
Now showing 1 - 10 of 11
Article Citation - WoS: 15Citation - Scopus: 15Spectral parameter power series for Sturm-Liouville equations on time scales(Elsevier Science inc, 2012) Erbe, Lynn; Mert, Raziye; Mert, Raziye; Peterson, Allan; 19485; MatematikWe 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.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; 19485; 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 Citation - WoS: 5Citation - Scopus: 5On disconjugacy and stability criteria for discrete Hamiltonian systems(Pergamon-elsevier Science Ltd, 2011) Mert, R.; Mert, Raziye; Zafer, A.; 19485; MatematikBy making use of new Lyapunov type inequalities, we establish disconjugacy and stability criteria for discrete Hamiltonian systems. The stability criteria are given when the system is periodic. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - Scopus: 3Oscillation for a nonlinear dynamic system on time scales(2011) Erbe, L.; Mert, Raziye; Mert, R.; 19485; 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 generalize some well-known results of Atkinson, Belohorec, Waltman, Hooker, Patula and others and also describe the relation to solutions of a delay-dynamic system. © 2011 Taylor & Francis.Article Citation - WoS: 14Citation - Scopus: 18Oscillation of even order nonlinear delay dynamic equations on time scales(Springer Heidelberg, 2013) Erbe, Lynn; Mert, Raziye; Mert, Raziye; Peterson, Allan; Zafer, Agacik; 19485; MatematikOne 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.Article Citation - WoS: 5Citation - Scopus: 5A halanay-type inequality on time scales in higher dimensional spaces(Element, 2014) Jia, Baoguo; Mert, Raziye; Erbe, Lynn; Mert, Raziye; 19485; MatematikIn 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.Article Citation - WoS: 0Citation - Scopus: 0Comparison theorems for even order dynamic equations on time scales(Dynamic Publishers, inc, 2014) Jia Baoguo; Mert, Raziye; Erbe, Lynn; Mert, Raziye; 19485; 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 Citation - WoS: 1Citation - Scopus: 0Time scale extensions of a theorem of Wintner on systems with asymptotic equilibrium(Taylor & Francis Ltd, 2011) Mert, R.; Mert, Raziye; Zafer, A.; 19485; MatematikWe consider quasilinear dynamic systems of the form[image omitted]where is a time scale, and provide extensions of a theorem of Wintner on systems with asymptotic equilibrium to arbitrary time scales. More specifically, we give sufficient conditions for the asymptotic equilibrium of the above system in the sense that for any given constant vector c, there is a solution satisfying[image omitted] Our results are new for difference equations, q-difference equations and many other time scale systems even though their analogous for differential equations have been known for some time.Article Citation - Scopus: 0On 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: 7Citation - Scopus: 10Oscillation of higher-order neutral dynamic equations on time scales(Springeropen, 2012) Mert, Raziye; Mert, Raziye; 19485; MatematikIn 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.
