# Existence and qualitative behavior of oscillatory solutions of second order linear ordinary differential equations

## Main Article Content

## Abstract

We consider the second order linear differential equation(A) (p(t)y′)′ + q(t)y = 0;which is oscillatory, under the assumption that p(t) and q(t) are positive, continuously differentiable and monotone functions on [0;1). After studying qualitative properties, including amplitudes and slopes, of oscillatory solutions, we establish the existence of three types of solutions of (A) referred to as moderately bounded, small of large oscillatory solutions. Essential use is made of pairs of quadratic forms P(t)y′(t)2 + Q(t)y(t)2, R(t)y′(t)2 + S(t)y(t)2, which are monotone for all possible solutions y(t) of (A) but have different monotonicity.

## Article Details

How to Cite

Yoshida, N., & Kusano, T.
(2017).
Existence and qualitative behavior of oscillatory solutions of second order linear ordinary differential equations.

*Acta Mathematica Universitatis Comenianae, 86*(1), 23-50. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/270/413
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