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Belohorec‐type oscillation theorem for second order sublinear dynamic equations on time scales
Authors:Lynn Erbe  Baoguo Jia  Allan Peterson
Institution:1. University of Nebraska‐Lincoln, Lincoln, Nebraska 68588 0130, USA;2. Zhongshan University, Guangzhou 51025, P. R. China
Abstract:Consider the Emden‐Fowler sublinear dynamic equation equation image (0.1) where $p\in C(\mathbb{T},R)$, where $\mathbb{T}$ is a time scale, 0 < α < 1. When p(t) is allowed to take on negative values, we obtain a Belohorec‐type oscillation theorem for (0.1). As an application, we get that the sublinear difference equation equation image (0.2) is oscillatory, if equation image and the sublinear q‐difference equation equation image (0.3) where $t\in q^{\mathbb{N}_0}, q>1$, is oscillatory, if equation image
Keywords:Oscillation  Emden‐Fowler equation  sublinear  MSC (2010) 34K11  39A10  39A99
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