carpathian_2022_38_2_327_335_001

New asymptotic results for half-linear differential equations with deviating argument


Baculíková, Blanka and Dzurina, Jozef


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carpathian_2022_38_2_327_335

In the paper, we study the oscillation of the half-linear second-order differential equations with deviating argument of the form

(E)   \begin{equation*} \left(r(t)(y'(t))^{\alpha}\right)'=p(t)y^{\alpha}(\tau(t)). \end{equation*}

We introduce new monotonic properties of nonoscillatory solutions and use them to offer new criteria for elimination of certain types of solutions.  The presented results essentially improve existing ones even for linear differential equations.

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Author(s)

  Dzurina, Jozef, Blanka, Baculíková

DOI

https://doi.org/10.37193/CJM.2022.02.05