G. A. Grigoryan, “Some properties of solutions of second-order linear ordinary differential equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 1, 2013, 69

Loading [MathJax]/jax/output/SVG/config.js

Trudy Instituta Matematiki i Mekhaniki UrO RAN

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2013, Volume 19, Number 1, Pages 69–80 (Mi timm900)

This article is cited in 7 scientific papers (total in 7 papers)

Some properties of solutions of second-order linear ordinary differential equations

G. A. Grigoryan

Institute of Mathematics, National Academy of Sciences of Armenia

Full-text PDF (194 kB) Citations (7)

References:

PDF

HTML

Abstract: The Riccati equation method is used to obtain lower and upper estimates for the distance between two consecutive zeros of a solution and the derivative of the solution to a second-order linear ordinary differential equation in terms of its coefficients. Oscillation conditions and a stability condition are proved, and a theorem on the asymptotic behavior of zeros of solutions to a second-order linear equation and on the asymptotic behavior of one of the solutions to this equation is established.

Keywords: Riccati equation, estimation of the distance between two consecutive zeroes, oscillation, nonoscillation, oscillation on a finite interval, asymptotic behavior, stability.

Received: 12.04.2012

Bibliographic databases:

Document Type: Article

UDC: 517.923

Language: Russian

Citation: G. A. Grigoryan, “Some properties of solutions of second-order linear ordinary differential equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 1, 2013, 69–80

Citation in format AMSBIB

\Bibitem{Gri13}

\by G.~A.~Grigoryan

\paper Some properties of solutions of second-order linear ordinary differential equations

\serial Trudy Inst. Mat. i Mekh. UrO RAN

\yr 2013

\vol 19

\issue 1

\pages 69--80

\mathnet{http://mi.mathnet.ru/timm900}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3408362}

\elib{https://elibrary.ru/item.asp?id=18839266}

Linking options:

https://www.mathnet.ru/eng/timm900

https://www.mathnet.ru/eng/timm/v19/i1/p69

This publication is cited in the following 7 articles:

Grigorian G.A., “Oscillation and Non-Oscillation Criteria For Linear Nonhomogeneous Systems of Two First-Order Ordinary Differential Equations”, J. Math. Anal. Appl., 507:1 (2022), 125734
Hasil P., Vesely M., “New Conditionally Oscillatory Class of Equations With Coefficients Containing Slowly Varying and Periodic Functions”, J. Math. Anal. Appl., 494:1 (2021), 124585
G. A. Grigorian, “Properties of solutions of the scalar Riccati equation with complex coefficients and some their applications”, Diff. Equat. Appl., 10:3 (2018), 277–298
G. A. Grigoryan, “Global solvability tests for a scalar Riccati equation with complex coefficients”, Differ. Equ., 53:4 (2017), 450–456
G. A. Grigorian, “Oscillatory criteria for the systems of two first-order linear differential equations”, Rocky Mt. J. Math., 47:5 (2017), 1497–1524
G. A. Grigoryan, “Criteria of global solvability for Riccati scalar equations”, Russian Math. (Iz. VUZ), 59:3 (2015), 31–42
G. A. Grigoryan, “On the stability of systems of two first-order linear ordinary differential equations”, Differ. Equ., 51:3 (2015), 283–292

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

Statistics & downloads:
Abstract page:	774
Full-text PDF :	220
References:	99
First page:	18

Что такое QR-код?

Registration to the website

Logotypes