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
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