Publication details
De la Vallee Poussin type inequality and eigenvalue problem for generalized half-linear differential equation
| Authors | |
|---|---|
| Year of publication | 2014 |
| Type | Article in Periodical |
| Magazine / Source | Arch. Math. (Brno) |
| MU Faculty or unit | |
| 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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