Oscillation of Linear Ordinary Differential Equations: on a Theorem by A. Grigoriev

@inproceedings{Yakovenko2004OscillationOL,
title={Oscillation of Linear Ordinary Differential Equations: on a Theorem by A. Grigoriev},
author={Sergei A Yakovenko},
year={2004}
}

We give a simplified proof and an improvement of a recent theorem by A. Grigoriev, placing an upper bound for the number of roots of linear combinations of solutions to systems of linear equations with polynomial or rational coefficients. 1. Background on counting zeros of solutions of linear ordinary differential equations 1.1. De la Valée Poussin theorem and Novikov’s counterexample. A linear nth order homogeneous differential equation y + a1(t) y (n−1) + · · · + an−1(t) y + an(t) y = 0, y… CONTINUE READING