Hille and Nehari type criteria for third-order dynamic equations |
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Authors: | L Erbe A Peterson SH Saker |
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Institution: | a Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0130, USA b Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt |
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Abstract: | In this paper, we extend the oscillation criteria that have been established by Hille E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948) 234-252] and Nehari Z. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957) 428-445] for second-order differential equations to third-order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. We consider several examples to illustrate our results. |
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Keywords: | Oscillation Third-order dynamic equations Time scales |
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