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Mat. Sb., 2008, Volume 199, Number 6, Pages 105–136 (Mi msb3860)  

This article is cited in 6 scientific papers (total in 6 papers)

Zeros of the Green's function for the de la Vallée-Poussin problem

Yu. V. Pokornyi

Voronezh State University

Abstract: The Green's function for the de la Vallée-Poussin problem
\begin{gather*} Lx\equiv x^{(n)}+p_1(t)x^{(n-1)}+…+p_n(t)x=f,
x(a_i)=A_i^{(0)}, x'(a_i)=A_i^{(1)}, …, x^{(\nu_i-1)}(a_i)=A_i^{(\nu_i-1)}, i= {1,…,m}, \end{gather*}
where $a=a_1<a_2<…<a_m=b$, $m\ge2$, $\sum\nu_i=n$, $p_i( \cdot )$ and $f( \cdot )\in L_1[a,b]$, is investigated. It is defined in the square $a\le t,s\le b$, and vanishes at the lines $t=a_i$, $i={1,…,m}$, $s=a$, $s=b$; it is proved that the orders of its zeros have uniform bounds.
Bibliography: 27 titles.

DOI: https://doi.org/10.4213/sm3860

Full text: PDF file (685 kB)
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English version:
Sbornik: Mathematics, 2008, 199:6, 891–921

Bibliographic databases:

UDC: 517.927
MSC: 34B27, 34B15
Received: 19.04.2007 and 16.11.2007

Citation: Yu. V. Pokornyi, “Zeros of the Green's function for the de la Vallée-Poussin problem”, Mat. Sb., 199:6 (2008), 105–136; Sb. Math., 199:6 (2008), 891–921

Citation in format AMSBIB
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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. Israilov S.V., Sagitov A.A., “Svoistva kolebatelnosti i statsionarnosti reshenii singulyarnykh differentsialnykh uravnenii”, Vestn. Tambovskogo un-ta. Ser.: Estestvennye i tekhnicheskie nauki, 15:2 (2010), 526–530  elib
    2. R. Ch. Kulaev, “O funktsii vliyaniya tsepochki sterzhnei s uprugimi oporami”, Vladikavk. matem. zhurn., 16:2 (2014), 49–61  mathnet
    3. R. Ch. Kulaev, “Usloviya ostsillyatsionnosti funktsii Grina razryvnoi kraevoi zadachi dlya uravneniya chetvertogo poryadka”, Vladikavk. matem. zhurn., 17:1 (2015), 47–59  mathnet
    4. V. V. Napalkov, A. U. Mullabaeva, “Kratnaya interpolyatsionnaya zadacha Valle Pussena”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 19:1 (2015), 63–77  mathnet  crossref  zmath  elib
    5. Kulaev R.Ch., “Oscillation of the Green Function of a Multipoint Boundary Value Problem For a Fourth-Order Equation”, Differ. Equ., 51:4 (2015), 449–463  crossref  mathscinet  zmath  isi  elib  scopus
    6. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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