## Conditional oscillation of half-linear differential equations with periodic coefficients.(English)Zbl 1212.34110

Summary: We show that the half-linear differential equation $\big [r(t)\Phi (x')\big ]' + \frac {s(t)}{t^p} \Phi (x) = 0$ with $$\alpha$$-periodic positive functions $$r, s$$ is conditionally oscillatory, i.e., there exists a constant $$K>0$$ such that the equation with $$\gamma s(t)/t^p$$ instead of $$s(t)/t^p$$ is oscillatory for $$\gamma > K$$ and nonoscillatory for $$\gamma < K$$.

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
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