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Mat. Sb., 1997, Volume 188, Number 11, Pages 121–159 (Mi msb282)  

This article is cited in 10 scientific papers (total in 10 papers)

Effective criteria for the strong sign-regularity and the oscillation property of the Green's functions of two-point boundary-value problems

G. D. Stepanov

Voronezh State Pedagogical University

Abstract: Necessary and sufficient conditions for strong sign-regularity and the oscillation property (in the sense of Gantmakher and Krein) of the Green's function of a two-point boundary eigenvalue problem are obtained. These conditions guarantee that even in a non-self-adjoint case the eigenvalues are real and have several other spectral properties similar to those of the classical Sturm–Liouville problem. The conditions are formulated in terms of the properties of a uniquely defined fundamental system of solutions of the differential equation. This makes it possible to verify them effectively using a computer and to establish, as the final result, the oscillation property of the Green's function and the corresponding spectral properties of the boundary-value problem in a large number of cases in which these properties could not be detected on the basis of previously known sufficient conditions.


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English version:
Sbornik: Mathematics, 1997, 188:11, 1687–1728

Bibliographic databases:

UDC: 517.927.2
MSC: 34B27, 34C10
Received: 17.10.1996

Citation: G. D. Stepanov, “Effective criteria for the strong sign-regularity and the oscillation property of the Green's functions of two-point boundary-value problems”, Mat. Sb., 188:11 (1997), 121–159; Sb. Math., 188:11 (1997), 1687–1728

Citation in format AMSBIB
\by G.~D.~Stepanov
\paper Effective criteria for the~strong sign-regularity and the~oscillation property of the~Green's functions of two-point boundary-value problems
\jour Mat. Sb.
\yr 1997
\vol 188
\issue 11
\pages 121--159
\jour Sb. Math.
\yr 1997
\vol 188
\issue 11
\pages 1687--1728

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    This publication is cited in the following articles:
    1. Stepanov G.D., “Ob odnom klasse kraevykh zadach s ostsillyatsionnymi svoistvami chasti spektra”, Dokl. RAN, 370:5 (2000), 591–594  mathnet  mathscinet  zmath  isi
    2. A. V. Borovskikh, “Sign Regularity Conditions for Discontinuous Boundary-Value Problems”, Math. Notes, 74:5 (2003), 607–618  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. Ya. Derr, “Neostsillyatsiya reshenii lineinykh differentsialnykh uravnenii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2009, no. 1, 46–89  mathnet  elib
    4. Kulaev R.Ch., “On the Nonoscillation of An Equation on a Graph”, Differ. Equ., 50:11 (2014), 1565–1566  crossref  mathscinet  zmath  isi  scopus  scopus
    5. R. Ch. Kulaev, “O funktsii vliyaniya tsepochki sterzhnei s uprugimi oporami”, Vladikavk. matem. zhurn., 16:2 (2014), 49–61  mathnet
    6. R. Ch. Kulaev, “Usloviya ostsillyatsionnosti funktsii Grina razryvnoi kraevoi zadachi dlya uravneniya chetvertogo poryadka”, Vladikavk. matem. zhurn., 17:1 (2015), 47–59  mathnet
    7. R. Ch. Kulaev, “Disconjugacy of fourth-order equations on graphs”, Sb. Math., 206:12 (2015), 1731–1770  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. Kulaev R.Ch., “Necessary and Sufficient Condition For the Positivity of the Green Function of a Boundary Value Problem For a Fourth-Order Equation on a Graph”, Differ. Equ., 51:3 (2015), 303–317  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Kulaev R.Ch., “Criterion For the Positiveness of the Green Function of a Many-Point Boundary Value Problem For a Fourth-Order Equation”, Differ. Equ., 51:2 (2015), 163–176  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    10. A. A. Vladimirov, “On the Problem of Oscillation Properties of Positive Differential Operators with Singular Coefficients”, Math. Notes, 100:6 (2016), 790–795  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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