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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 1, Pages 5–22 (Mi izv7800)  

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

On the continuous invertibility and the Fredholm property of differential operators with multi-valued impulse effects

V. B. Didenko

Voronezh State University

Abstract: We obtain necessary and sufficient conditions for the continuous invertibility and the Fredholm property of operators generated by a family of evolution operators, with boundary conditions given by a linear relation and impulse effects also given by a linear relation.

Keywords: continuous invertibility, Fredholm property, family of evolution operators, linear relation, impulse effect.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00378


DOI: https://doi.org/10.4213/im7800

Full text: PDF file (539 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2013, 77:1, 3–19

Bibliographic databases:

UDC: 517.9
MSC: Primary 34A37; Secondary 47E05, 93B99
Received: 09.06.2011
Revised: 18.11.2011

Citation: V. B. Didenko, “On the continuous invertibility and the Fredholm property of differential operators with multi-valued impulse effects”, Izv. RAN. Ser. Mat., 77:1 (2013), 5–22; Izv. Math., 77:1 (2013), 3–19

Citation in format AMSBIB
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  • https://doi.org/10.4213/im7800
  • http://mi.mathnet.ru/eng/izv/v77/i1/p5

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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. V. M. Bruk, “On Linear Relations Generated by an Integro-Differential Equation with Nevanlinna Measure in the Infinite-Dimensional Case”, Math. Notes, 96:1 (2014), 10–25  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. V. B. Didenko, “O sostoyaniyakh obratimosti lineinykh differentsialnykh operatorov s neogranichennymi periodicheskimi koeffitsientami”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:2 (2014), 136–144  mathnet  crossref  elib
    3. V. M. Bruk, “Dissipative expansions of a symmetric relation generated by a system of integral equations with operator measures”, Russian Math. (Iz. VUZ), 58:12 (2014), 7–22  mathnet  crossref
    4. V. M. Bruk, “Invertibility of linear relations generated by integral equation with operator measures”, Ufa Math. J., 6:4 (2014), 48–59  mathnet  crossref
    5. A. Yu. Duplishcheva, “About Conditions of Invertibility of Difference Operators of the Second Order”, J. Math. Sci., 213:6 (2016), 832–837  mathnet  crossref
    6. A. Yu. Duplischeva, “O differentsialnykh operatorakh i matritsakh vtorogo poryadka”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:1 (2015), 31–37  mathnet  crossref  elib
    7. A. G. Baskakov, V. B. Didenko, “Spectral analysis of differential operators with unbounded periodic coefficients”, Differ. Equ., 51:3 (2015), 325  crossref  crossref  zmath  isi  elib  elib  scopus
    8. A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. Math., 82:1 (2018), 1–13  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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