Rocky Mountain Journal of Mathematics

Oscillatory criteria forthe systems of two first-orderlinear differential equations

G.A. Grigorian

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Abstract

A definition of strict oscillation of the system of two first-order linear ordinary differential equations is given. It is shown that oscillation follows from strict oscillation of its system, but strict oscillation does not follow. Sturm-type theorems are proven. Oscillatory and strict oscillatory criteria in terms of coefficients of the system are obtained.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 5 (2017), 1497-1524.

Dates
First available in Project Euclid: 22 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1506045622

Digital Object Identifier
doi:10.1216/RMJ-2017-47-5-1497

Mathematical Reviews number (MathSciNet)
MR3705762

Subjects
Primary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory

Keywords
The Riccati equation normal and marginal solutions null-elements null-classes oscillation strict oscillation Sturm type theorems Ph.~Hartman's oscillatory criterion

Citation

Grigorian, G.A. Oscillatory criteria forthe systems of two first-orderlinear differential equations. Rocky Mountain J. Math. 47 (2017), no. 5, 1497--1524. doi:10.1216/RMJ-2017-47-5-1497. https://projecteuclid.org/euclid.rmjm/1506045622


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