Baoguo Jia
Abstract:
Consider the second-order nonlinear dynamic equation
where
is the backward jump operator.
We obtain a Kwong-Wong-type integral equation, that is:
If
is a nonoscillatory solution of the above equation on
,
then the integral equation
is satisfied for
,
where
,
and
.
As an application, we show that the superlinear dynamic equation
is oscillatory, under certain conditions.
Submitted July 21, 2011. Published September 29, 2011.
Math Subject Classifications: 34K11, 39A10, 39A99.
Key Words: Nonlinear dynamic equation; integral equation;
nonoscillatory solution.
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Baoguo Jia School of Mathematics and Computer Science Zhongshan University, Guangzhou, 510275, China email: mcsjbg@mail.sysu.edu.cn |
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