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

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Authors

BÁŇA Libor DOŠLÝ Ondřej

Year of publication 2014
Type Article in Periodical
Magazine / Source Arch. Math. (Brno)
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords Generalized half-linear differential equation; de la Vallee Poussin inequality; half-linear Euler differential equation
Description We study the generalized half-linear second order differential equation via the associated Riccati type differential equation and Pr\"ufer transformation. We establish a de la Vall\'ee 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 we study a Dirichlet eigenvalue problem associated with the investigated half-linear equation.
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