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Keywords:
generalized half-linear differential equation; de la Vallée Poussin inequality; half-linear Euler differential equation; Dirichlet eigenvalue problem
generalized half-linear differential equation; de la Vallée Poussin inequality; half-linear Euler differential equation; Dirichlet eigenvalue problem
Summary:
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.
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