Electron. J. Diff. Eqns., Vol. 2005(2005), No. 27, pp. 1-9.

Kamenev-type oscillation criteria for second-order quasilinear differential equations

Zhiting Xu, Yong Xia

Abstract:
We obtain Kamenev-type oscillation criteria for the second-order quasilinear differential equation
$$ (r(t)|y'(t)|^{\alpha-1}y'(t))'+ p(t)|y(t)|^{\beta-1}y(t)=0 \,. $$
The criteria obtained extend the integral averaging technique and include earlier results due to Kamenev, Philos and Wong.

Submitted August 11, 2004. Published March 6, 2005.
Math Subject Classifications: 34C10, 34C15.
Key Words: Oscillation; second order quasilinear differential equation; integral operator.

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Zhiting Xu
School of Mathematical Sciences, South China Normal University
Guangzhou, 510090, China
email: xztxhyyj@pub.guangzhou.gd.cn
Yong Xia
Department of Mathematics, Dongguan Institute of Technology
Dongguan, 511700, China
email: xiay@dgut.edu.cn

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