## Oscillation criteria for second-order nonlinear dynamic equations on time scales.(English)Zbl 1050.34042

The authors consider the nonlinear dynamic equation $(p(t) x^\Delta(t))^\Delta+ q(t) (f\circ x^\sigma)= 0\tag{1}$ on time scales, where $$p$$, $$q$$ are positive, real-valued, right-dense, continuous functions, and $$f: \mathbb{R}\to\mathbb{R}$$ is continuous and satisfies $$xf(x)> 0$$ and $$| f(x)|\geq K| x|$$ for $$x\neq 0$$, for some $$K>0$$. The authors consider the two cases $$\int^\infty_{t_0}{\Delta t\over p(t)}=\infty$$, $$\int^\infty_{t_0}{\Delta t\over p(t)}<\infty$$. They present oscillation criteria for (1) by using generalized Riccati transformation techniques and generalized exponential functions.

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 39A11 Stability of difference equations (MSC2000)
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