Approximability of the zeros of a function by the zeros of one of its asymptotic representations. Application to the solutions of linear second order differential equations
type: Item
instance of: scholarly article
title: Approximability of the zeros of a function by the zeros of one of its asymptotic representations. Application to the solutions of linear second order differential equations
zbMATH Open document ID: 0556.34059
author: Anna Maria Bresquar
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1983-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/107909
review text: Given a \(C^ 1\) function f(x) defined on \(0\leq x<\infty\), which is ''regularly oscillatory'' (the zeros of f(x) and of f'(x) alternate), with bounded derivative, satisfying a condition of separation of zeros, having a differentiable asymptotic expansion, it is proved that the zeros of this asymptotic expansion approximate the zeros of f(x). This result is then applied to the solutions of differential equations of the form \((p(t)y'(t))'+q(t)y(t)=0\), satisfying \(\int^{\infty}\sqrt{q(t)/p(t)} dt=+\infty\). Several counterexamples show that the assumptions in the corresponding theorems are needed.
Mathematics Subject Classification ID: 34E05
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 3886341
zbMATH Keywords: regularly oscillatory function
zbMATH Keywords: counterexamples
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3886341