Electronic Journal of Differential Equations, Vol. 2011 (2011), No. 125, pp. 1-14. Title: Kwong-Wong-type integral equation on time scales Author: Baoguo Jia (Zhongshan Univ., Guangzhou, China) Abstract: Consider the second-order nonlinear dynamic equation $$[r(t)x^\Delta(\rho(t))]^\Delta+p(t)f(x(t))=0,$$ where $p(t)$ is the backward jump operator. We obtain a Kwong-Wong-type integral equation, that is: If $x(t)$ is a nonoscillatory solution of the above equation on $[T_0,\infty)$, then the integral equation $$\frac{r^\sigma(t)x^\Delta(t)}{f(x^\sigma(t))} =P^\sigma(t)+\int^\infty_{\sigma(t)}\frac{r^\sigma(s) [\int^1_0f'(x_h(s))dh][x^\Delta(s)]^2}{f(x(s)) f(x^\sigma(s))}\Delta s$$ is satisfied for $t\geq T_0$, where $P^\sigma(t)=\int^\infty_{\sigma(t)}p(s)\Delta s$, and $x_h(s)=x(s)+h\mu(s)x^\Delta(s)$. As an application, we show that the superlinear dynamic equation $$[r(t)x^{\Delta}(\rho(t))]^\Delta+p(t)f(x(t))=0,$$ 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.