Rocky Mountain Journal of Mathematics

Some properties of the solutions of third order linear ordinary differential equations

G.A. Grigorian

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The method of Riccati equations is used to study some properties of third order linear ordinary differential equations. Some criteria of asymptotic behavior and non stability of solution of this equation are obtained. Two oscillatory criteria are proved.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 1 (2016), 147-168.

Dates
First available in Project Euclid: 23 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1464035857

Digital Object Identifier
doi:10.1216/RMJ-2016-46-1-147

Mathematical Reviews number (MathSciNet)
MR3506083

Zentralblatt MATH identifier
1353.34012

Subjects
Primary: 34C10: Oscillation theory, zeros, disconjugacy and comparison theory 34C99: None of the above, but in this section

Keywords
Riccati equations criterion of Raus-Hurwitz asymptotic behavior non stability oscillation

Citation

Grigorian, G.A. Some properties of the solutions of third order linear ordinary differential equations. Rocky Mountain J. Math. 46 (2016), no. 1, 147--168. doi:10.1216/RMJ-2016-46-1-147. https://projecteuclid.org/euclid.rmjm/1464035857


Export citation

References

  • L. Erbe, Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equations, Pac. J. Math. 64 (1976), 369–385.
  • Linn H. Erbe, Quingkai Kong and Sigui Ruan, Kamenev tipe theorems for second order matrix differential systems, Proc. Amer. Math. Soc. 117 (1983), 957–962.
  • G.A. Grigorian, On two comparison tests for second-order linear ordinary differential equations, Diff. Urav. 47 (2011), 1225–1240 (in Russian); Diff. Equat. 47 (2011), 1237–1252, (in English).
  • ––––, Two comparison criteria for scalar Riccati equations and some applications, Izv. Math. 11 (2012), 20–35.
  • G.D. Jones, Oscillatory behavior of third order differential equations, Proc. Amer. Math. Soc. 41 (1974), 133–136.
  • E. Kamke, Handbook of ordinary differential equations, Gos. Izdat., Moscow, 1953.
  • I.T. Kiguradze and T.A. Chanturia, The asymptotic behavior of the solutions of nonlinear ordinary differentia equations, Nauka, Moscow, 1990.
  • V.A. Kondratev, On the zeroes of the equation $y^{(n)} +p(x)y=0$, DAN USSR 120 (1958), 1180–1182.
  • A.I. Kostrikin, Introduction to algebra, Nauka, Moscow, 1977.
  • A.C. Lazer, The behavior of solutions of the differential equations $y''' + P(x) y' +q(x) y = 0$, Pac. J. Math. 17 (1966), 435–466.
  • N. Parhi and P. Das, Asymptotic property of solutions of a class of third-order differential equations, Proc. Amer. Math. Soc. 110 (1990), 387–393.
  • C.A. Swanson, Comparison and oscillation theory of linear differential equations, Academic Press, New York, 1968.