Electron. J. Diff. Equ., Vol. 2015 (2015), No. 71, pp. 1-12.

Theorems of Kiguradze-type and Belohorec-type revisited on time scales

Hongwu Wu, Baoguo Jia, Lynn Erbe

This article concerns the oscillation of second-order nonlinear dynamic equations. By using generalized Riccati transformations, Kiguradze-type and Belohorec-type oscillation theorems are obtained on an arbitrary time scale. Our results cover those for differential equations and difference equations, and provide new oscillation criteria for irregular time scales. Some examples are given to illustrate our results.

Submitted December 14, 2014. Published March 24, 2015.
Math Subject Classifications: 34K11, 39A10, 39A99.
Key Words: Superlinear; sublinear; time scales; second order; oscillation.

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Hongwu Wu
School of Mathematics
South China University of Technology
Guangzhou 510640, China
email: hwwu@scut.edu.cn
Baoguo Jia
School of Mathematics and Computer Science
Zhongshan University
Guangzhou 510275, China
email: mcsjbg@mail.sysu.edu.cn
Lynn Erbe
Department of Mathematics
University of Nebraska-Lincoln
Lincoln, NE 68588-0130, USA
email: lerbe@unl.edu

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