Geodesic
De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation
Archivum mathematicum, Tome 50 (2014) no. 4, pp. 193-203

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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 we study a Dirichlet eigenvalue problem associated with the investigated half-linear equation.
DOI : 10.5817/AM2014-4-193
Classification : 34C10
Keywords: generalized half-linear differential equation; de la Vallée Poussin inequality; half-linear Euler differential equation; Dirichlet eigenvalue problem 
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Báňa, Libor; Došlý, Ondřej. De la Vallée Poussin type inequality and eigenvalue problem for generalized half-linear differential equation. Archivum mathematicum, Tome 50 (2014) no. 4, pp. 193-203. doi: 10.5817/AM2014-4-193

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