Application of de La Vallée Poussin type inequalities to half-linear Euler type equations

Abstract

The paper is devoted to the application of de la Vallée Poussin type inequalities to half-linear differential Euler type equations. Four studied equations seen as perturbations of the nonoscillatory Euler equation with the oscillation constant are considered, and a new theorem for the cases where the perturbation is in both terms is presented. Several different corollaries of de la Vallée Poussin type inequalities for Euler type equations, which can help in estimating the distance between consecutive zero points of their solutions, are formulated.