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Browsing by Author "Peterson, Allan"

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    Citation - WoS: 14
    Citation - Scopus: 18
    Oscillation of even order nonlinear delay dynamic equations on time scales
    (Springer Heidelberg, 2013) Erbe, Lynn; Mert, Raziye; Mert, Raziye; Peterson, Allan; Zafer, Agacik; 19485; Matematik
    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.
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    Article
    Citation - WoS: 15
    Citation - Scopus: 15
    Spectral parameter power series for Sturm-Liouville equations on time scales
    (Elsevier Science inc, 2012) Erbe, Lynn; Mert, Raziye; Mert, Raziye; Peterson, Allan; 19485; Matematik
    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.