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Mat. Zametki, 1968, Volume 4, Issue 5, Pages 533–540 (Mi mz6772)  

This article is cited in 3 scientific papers (total in 3 papers)

On estimates for the Green's function for a multipoint boundary problem

Yu. V. Pokornyi

Voronezh State University

Abstract: We obtain new estimates for the Green's function $G(t, s)$ for a boundary problem of the Vallée-Poussin type: under certain hypotheses we prove the existence of non-negative functions $g(t)$, $h(t)$, $u(t)$ such that $g(t)h(s)\le|G(t,s)|\le g(t)$ and $|G(t,s)|\ge u(t)\max\limits_\tau|G(\tau,s)|$, where $h(t)$ and $u(t)$ are positive on sets of positive measure. These estimates allow us to apply effectively the methods of the theory of cones to investigate non-linear boundary problems.

Full text: PDF file (631 kB)

English version:
Mathematical Notes, 1968, 4:5, 810–814

Bibliographic databases:

UDC: 517.9
Received: 11.12.1967

Citation: Yu. V. Pokornyi, “On estimates for the Green's function for a multipoint boundary problem”, Mat. Zametki, 4:5 (1968), 533–540; Math. Notes, 4:5 (1968), 810–814

Citation in format AMSBIB
\Bibitem{Pok68}
\by Yu.~V.~Pokornyi
\paper On estimates for the Green's function for a~multipoint boundary problem
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 5
\pages 533--540
\mathnet{http://mi.mathnet.ru/mz6772}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=236453}
\zmath{https://zbmath.org/?q=an:0176.05102|0167.07304}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 5
\pages 810--814
\crossref{https://doi.org/10.1007/BF01111315}


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

    This publication is cited in the following articles:
    1. A. Yu. Levin, “Non-oscillation of solutions of the equation $x^{(n)}+p_1(t)x^{(n-1)}+…+p_n(t)x=0$”, Russian Math. Surveys, 24:2 (1969), 43–99  mathnet  crossref  mathscinet  zmath
    2. P. P. Zabreiko, M. A. Krasnosel'skii, Yu. V. Pokornyi, “On a class of linear positive operators”, Funct. Anal. Appl., 5:4 (1971), 272–279  mathnet  crossref  mathscinet  zmath
    3. Yu. V. Pokornyi, “Zeros of the Green's function for the de la Vallée-Poussin problem”, Sb. Math., 199:6 (2008), 891–921  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Математические заметки Mathematical Notes
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