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Hassan, Taher S.; Erbe, Lynn; Peterson, Allan

Oscillation of second order superlinear dynamic equations with damping on time scales. (English) Zbl 1189.34133

Comput. Math. Appl. 59, No. 1, 550-558 (2010).
Summary: This paper concerns the oscillation of solutions to the second order superlinear dynamic equation with damping \((r(t)x\Delta (t))\Delta +p(t)x\Delta (t)+q(t)f(x\sigma (t))=0\) , on a time scale \(\mathbb{T}\) which is unbounded above. No sign conditions are imposed on \(r(t)\), \(p(t)\) and \(q(t)\). The function \(f\in C(\mathbb{R},\mathbb{R})\) is assumed to satisfy \(xf(x)>0\) and \(f'(x)>0\), for \(x\neq 0\). We illustrate the results by several examples.

Cited in 2 Reviews
Cited in 10 Documents

MSC:

34K11 Oscillation theory of functional-differential equations
39A10 Additive difference equations
39A99 Difference equations

Keywords:

oscillation; superlinear dynamic equations; time scales
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\textit{T. S. Hassan} et al., Comput. Math. Appl. 59, No. 1, 550--558 (2010; Zbl 1189.34133)
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References:

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