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

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.

MSC:

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

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