Oscillation criteria for a forced second-order nonlinear dynamic equation. (English) Zbl 1168.34025

Erbe, L.; Peterson, A.; Saker, S. H.

J. Difference Equ. Appl. 14, No. 10-11, 997-1009 (2008).

By means of a Riccati technique and the function class \(\{u\in C^1_{rd}({\mathbb{T}}): u(t)\not\equiv 0\) on \([a, b]\), \(u(a)=u(b)=0\}\), the authors establish new interval oscillation criteria for forced second-order nonlinear dynamic equations on time scales of the form
\[ \left(p(t)x^{\Delta}(t)\right)^{\Delta}+q(t)| x^\sigma(t)| ^\gamma \text{sgn}\,x^\sigma(t)=f(t),\quad t\in \mathbb{T}, \]
where \({\mathbb{T}}\) is a time scale and \(\gamma\geq 1\) is a constant. Four interesting examples are included to show the significance of the results.

Reviewer: Qiru Wang (Guangzhou)

MSC:

34C10	Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
39A10	Additive difference equations

Keywords:

oscillation; second-order nonlinear dynamic equations; forced Emden-Fowler type; time scale

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