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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, Issue 1, Pages 46–89 (Mi vuu3)  

This article is cited in 9 scientific papers (total in 10 papers)

MATHEMATICS

Disconjugacy of solutions of linear differential equations

V. Ya. Derr

Udmurt State University

Abstract: It is an expository article devoted to the disconjugacy theory for decisions of the homogeneous differential equation of $n$-th order. We give new proofs of some basic results of this theory, such as sufficient conditions for disconjugacy, some implications from disconjugacy, properties of disconjugate equations. We also give new sufficient conditions of disconjugacy for second order differential equations.

Keywords: disconjugacy, conjugate points, factorization, generalized Rolle's Theorem, multi-point Vallee Poussin's boundary value problem, Green's function.

Full text: PDF file (454 kB)
References: PDF file   HTML file
UDC: 517.2+517.5
MSC: 34K11
Received: 01.09.2008

Citation: V. Ya. Derr, “Disconjugacy of solutions of linear differential equations”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, no. 1, 46–89

Citation in format AMSBIB
\Bibitem{Der09}
\by V.~Ya.~Derr
\paper Disconjugacy of solutions of linear differential equations
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2009
\issue 1
\pages 46--89
\mathnet{http://mi.mathnet.ru/vuu3}
\elib{http://elibrary.ru/item.asp?id=12867775}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. S. D. Buntov, N. I. Leonov, E. L. Tonkov, N. N. Petrov, A. A. Gryzlov, B. P. Kondratev, A. I. Karpov, A. V. Borisov, D. L. Fedorov, “Vasilii Yakovlevich Derr. K yubileyu”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2010, no. 1, 133–136  mathnet
    2. Islamov G.G., Kogan Yu.V., “K voprosu o chebyshevskikh sistemakh”, Izvestiya Instituta matematiki i informatiki Udmurtskogo gosudarstvennogo universiteta, 2012, no. 1, 62–63  mathnet  zmath  elib
    3. Kulaev R.Ch., “on the Nonoscillation of An Equation on a Graph”, Differ. Equ., 50:11 (2014), 1565–1566  crossref  mathscinet  zmath  isi  elib  scopus
    4. I. G. Kim, “Neostsillyatsiya reshenii differentsialnogo uravneniya vtorogo poryadka s obobschennymi funktsiyami Kolombo v koeffitsientakh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:1 (2015), 21–28  mathnet  elib
    5. R. Ch. Kulaev, “Usloviya ostsillyatsionnosti funktsii Grina razryvnoi kraevoi zadachi dlya uravneniya chetvertogo poryadka”, Vladikavk. matem. zhurn., 17:1 (2015), 47–59  mathnet
    6. R. Ch. Kulaev, “Disconjugacy of fourth-order equations on graphs”, Sb. Math., 206:12 (2015), 1731–1770  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    7. R. Ch. Kulaev, “Comparison theorems for Green function of a fourth order boundary value problem on a graph”, Ufa Math. J., 7:4 (2015), 94–103  mathnet  crossref  isi  elib
    8. I. S. Orlova, “Linearizatsiya differentsialnykh uravnenii Pfaffa dlya uslovnykh kvantilei mnogomernykh veroyatnostnykh raspredelenii”, Vestn. SamGU. Estestvennonauchn. ser., 2015, no. 10(132), 29–39  mathnet  elib
    9. R. Ch. Kulaev, “On the disconjugacy property of an equation on a graph”, Siberian Math. J., 57:1 (2016), 64–73  mathnet  crossref  crossref  mathscinet  isi  elib
    10. V. S. Klimov, “O lokalno vypuklykh krivykh”, Model. i analiz inform. sistem, 24:5 (2017), 567–577  mathnet  crossref  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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