Previous |  Up |  Next


Title: On quadratically integrable solutions of the second order linear equation (English)
Author: Chantladze, T.
Author: Kandelaki, N.
Author: Lomtatidze, A.
Language: English
Journal: Archivum Mathematicum
ISSN: 0044-8753 (print)
ISSN: 1212-5059 (online)
Volume: 37
Issue: 1
Year: 2001
Pages: 57-62
Summary lang: English
Category: math
Summary: Integral criteria are established for $\dim V_i(p)=0$ and $\dim V_i(p)=1, i\in \lbrace 0,1\rbrace $, where $V_i(p)$ is the space of solutions $u$ of the equation \[ u^{\prime \prime }+p(t)u=0 \] satisfying the condition \[ \int ^{+\infty }\frac{u^2(s)}{s^i}ds<+\infty \,. \] (English)
Keyword: second order linear equation
Keyword: quadratically integrable solutions
Keyword: vanishing at infinity solutions
MSC: 34C11
idZBL: Zbl 1090.34537
idMR: MR1822762
Date available: 2008-06-06T22:28:18Z
Last updated: 2012-05-10
Stable URL:
Reference: [1] Wintner A.: On the non-existence of conjugate points.Amer. J. Math. 73 (1951), 368–380. MR 0042005
Reference: [2] Kneser A.: Untersuchung und asymptotische Darstellung der Integrale gewisser Differentialgleichungen bei grossen reelen Werten des Arguments.J. Reine Angew. Math. 116 (1896), 178–212.
Reference: [3] Kiguradze I.T., Chanturia T.A.: Asymptotic properties of solutions of nanautonomous ordinary differential equations.Kluwer Academic Publishers, Dordrecht–Boston–London, 1992.
Reference: [4] Kiguradze I.T., Shekhter B.L.: Singular boundary value problems for second order differential “Current Problems in Mathematics: Newest Results,” vol. 30, pp. 105–201, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyzn. Inst. Nauchn. i Tekhn. Inform., Moscow, 1987. MR 0925830
Reference: [5] Chantladze T., Kandelaki N., Lomtatidze A.: Oscillation and nonoscillation criteria for second order linear equations.Georgian Math. J. 6 (1999), No 5, 401–414. MR 1692963


Files Size Format View
ArchMathRetro_037-2001-1_7.pdf 303.9Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo