Electron. J. Diff. Equ., Vol. 2013 (2013), No. 54, pp. 1-10.

Existence of non-oscillatory solutions for second-order advanced half-linear differential equations

Aijun Cheng, Zhiting Xu

Abstract:
In this article, we establish the necessary and sufficient conditions for existence of non-oscillatory solutions for the second-order advanced half-linear differential equation
$$ \big(r(t)|x'(t)|^{\alpha-1}x'(t)\big)'+p(t)|x(h(t)\big)|^{\alpha-1}x(h(t))=0, \quad t\geq t_0. $$
The obtained results generalize some well-known theorems in the literature

Submitted August 4, 2012. Published February 21, 2013.
Math Subject Classifications: 34C10, 34C55.
Key Words: Oscillation; nonoscillation; half-linear; advanced differential equation.

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Aijun Cheng
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: chengaijun@163.com
Zhiting Xu
School of Mathematical Sciences
South China Normal University
Guangzhou 510631, China
email: xuzhit@126.com

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