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Mat. Sb., 2004, Volume 195, Number 9, Pages 3–18 (Mi msb842)  

This article is cited in 8 scientific papers (total in 8 papers)

Volterra inequalities in function spaces

E. S. Zhukovskii

Tambov State University

Abstract: We present results on local solubility, extendability of solutions, and the existence of upper and lower solutions of equations with monotonic generalized Volterra operators in Banach function spaces. These results are analogous to the well-known theorems on the integral and differential inequality and can be used for estimating solutions of various functional-differential equations.

DOI: https://doi.org/10.4213/sm842

Full text: PDF file (322 kB)
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English version:
Sbornik: Mathematics, 2004, 195:9, 1235–1251

Bibliographic databases:

UDC: 517.929
MSC: Primary 34K30, 45N05; Secondary 34K35, 45D05, 47H07, 47H10, 47H30, 47J25
Received: 08.12.2003

Citation: E. S. Zhukovskii, “Volterra inequalities in function spaces”, Mat. Sb., 195:9 (2004), 3–18; Sb. Math., 195:9 (2004), 1235–1251

Citation in format AMSBIB
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\paper Volterra inequalities in~function spaces
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\pages 3--18
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\yr 2004
\vol 195
\issue 9
\pages 1235--1251
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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. E. S. Zhukovskii, “Continuous dependence on parameters of solutions to Volterra's equations”, Sb. Math., 197:10 (2006), 1435–1457  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. E. S. Zhukovskii, M. J. Alves, “Abstract Volterra operators”, Russian Math. (Iz. VUZ), 52:3 (2008), 1–14  mathnet  crossref  mathscinet  zmath  elib
    3. Zhukovskaya T.V., Zhukovskii E.S., “Ob odnom podkhode k opredeleniyu ponyatiya volterrovogo operatora”, Vestn. Tambovskogo un-ta. Ser.: Estestvennye i tekhnicheskie nauki, 14:1 (2009), 308–318  elib
    4. A. V. Chernov, “Pointwise Estimation of the Difference of the Solutions of a Controlled Functional Operator Equation in Lebesgue Spaces”, Math. Notes, 88:2 (2010), 262–274  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Penkov V.B., Zhukovskaya T.V., Satalkina L.V., “O razreshimosti i otsenkakh reshenii differentsialnogo uravneniya s zapazdyvaniem, zavisyaschim ot iskomoi funktsii”, Vestnik Tambovskogo universiteta. Seriya: Estestvennye i tekhnicheskie nauki, 16:3 (2011), 748–751  mathscinet  elib
    6. A. V. Chernov, “A Generalization of Bihari's Lemma to the Case of Volterra Operators in Lebesgue Spaces”, Math. Notes, 94:5 (2013), 703–714  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. Zhukovskiy E.S., “On ordered-covering mappings and implicit differential inequalities”, Differ. Equ., 52:12 (2016), 1539–1556  crossref  mathscinet  zmath  isi  scopus
    8. E. S. Zhukovskii, Kh. M. T. Takhir, “Ob usloviyakh polozhitelnosti funktsii Koshi funktsionalno-differentsialnykh uravnenii”, Izv. vuzov. Matem., 2018, no. 11, 75–81  mathnet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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