## Two-parametric conditionally oscillatory half-linear differential equations.(English)Zbl 1217.34054

Summary: We study perturbations of the nonoscillatory half-linear differential equation
$(r(t)\Phi(x'))'+c(t)\Phi(x)=0,$
$$\Phi(x):=|x|^{p-2}x,$$ $$p>1$$. We find explicit formulas for the functions $$\widehat r$$, $$\widehat c$$ such that the equation
$[(r(t)+\lambda\widehat r(t)) \Phi(x')]'+[c(t)+\mu\widehat c(t)] \Phi (x)=0$
is conditionally oscillatory, that is, there exists a constant $$\gamma$$ such that the previous equation is oscillatory if $$\mu-\lambda>\gamma$$ and nonoscillatory if $$\mu-\lambda <\gamma$$. The obtained results extend previous results concerning two-parametric perturbations of the half-linear Euler differential equation.

### MSC:

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

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