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

• Autoři: BÁŇA Libor; DOŠLÝ Ondřej
• Rok publikování: 2014
• Druh: Článek v odborném periodiku
• Časopis / Zdroj: Arch. Math. (Brno)
• Fakulta / Pracoviště MU: Přírodovědecká fakulta
• Obor: Obecná matematika
• Klíčová slova: Generalized half-linear differential equation; de la Vallee Poussin inequality; half-linear Euler differential equation
• Popis: 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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