Geodesic
Kwong-wong-type integral equation on time scales
Electronic journal of differential equations, Tome 2011 (2011)
Consider the second-order nonlinear dynamic equation

$ [r(t)x^\Delta(\rho(t))]^\Delta+p(t)f(x(t))=0, $

where

$ \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

$ [r(t)x^{\Delta}(\rho(t))]^\Delta+p(t)f(x(t))=0, $

is oscillatory, under certain conditions.
Classification : 34K11, 39A10, 39A99
Keywords: nonlinear dynamic equation, integral equation, nonoscillatory solution 
@article{EJDE_2011__2011__a98,
     author = {Jia,  Baoguo},
     title = {Kwong-wong-type integral equation on time scales},
     journal = {Electronic journal of differential equations},
     year = {2011},
     volume = {2011},
     zbl = {1266.34143},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a98/}
}
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Jia,  Baoguo. Kwong-wong-type integral equation on time scales. Electronic journal of differential equations, Tome 2011 (2011). http://geodesic.mathdoc.fr/item/EJDE_2011__2011__a98/