Title

Fite-Hille-Wintner-Type Oscillation Criteria for Second-Order Half-Linear Dynamic Equations with Deviating Arguments

Abstract

We study oscillatory behavior of solutions to a class of second-order half-linear dynamic equations with deviating arguments under the assumptions that allow applications to dynamic equations with delayed and advanced arguments. Several improved Fite-Hille-Wintner-type criteria are obtained that do not need some restrictive assumptions required in related results. Illustrative examples and conclusions are presented to show that these criteria are sharp for differential equations and provide sharper estimates for oscillation of corresponding q-difference equations.

Department(s)

Mathematics and Statistics

Comments

The authors express their sincere gratitude to the editors and anonymous referee for the careful reading of the original manuscript and useful comments that helped to improve the presentation of the results and accentuate important details. This research is supported by Research Deanship of University of Hail (Grant No. 150486 ), NNSF of P. R. China (Grant No. 61503171 ), CPSF (Grant No. 2015M582091 ), NSF of Shandong Province (Grant No. ZR2016JL021 ), DSRF of Linyi University (Grant No. LYDX2015BS001 ), and the AMEP of Linyi University, P. R. China .

Keywords and Phrases

Advanced argument; Delayed argument; Half-linear; Oscillation behavior; Second-order dynamic equation; Time scale

International Standard Serial Number (ISSN)

0019-3577

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2018 Royal Dutch Mathematical Society (KWG), All rights reserved.

Publication Date

01 Apr 2018

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