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Zbl 1168.34025
Erbe, L.; Peterson, A.; Saker, S.H.
Oscillation criteria for a forced second-order nonlinear dynamic equation.
(English)
[J] J. Difference Equ. Appl. 14, No. 10-11, 997-1009 (2008). ISSN 1023-6198

By means of a Riccati technique and the function class $\{u\in C^1_{rd}({\Bbb{T}}): u(t)\not\equiv 0$ 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 $$\left(p(t)x^{\Delta}(t)\right)^{\Delta}+q(t)\vert x^\sigma(t)\vert ^\gamma \text {sgn}\,x^\sigma(t)=f(t),\quad t\in \Bbb{T},$$ where ${\Bbb{T}}$ is a time scale and $\gamma\ge 1$ is a constant. Four interesting examples are included to show the significance of the results.
[Qiru Wang (Guangzhou)]
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.
39A10 Difference equations

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

Cited in: Zbl 1205.34134

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