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De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation

Libor BáňaOndřej Došlý — 2014

Archivum Mathematicum

We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Prüfer transformation. We establish a de la Vallée Poussin type inequality for the distance of consecutive zeros of a nontrivial solution and this result we apply to the “classical” half-linear differential equation regarded as a perturbation of the half-linear Euler differential equation with the so-called critical oscillation constant. In the second part of the paper...

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