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CMFD, 2007, Volume 21, Pages 5–36 (Mi cmfd75)  

This article is cited in 7 scientific papers (total in 7 papers)

On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics

E. M. Varfolomeev

Peoples Friendship University of Russia

Abstract: Quasilinear parabolic functional differential equations containing multiple transformations of spatial variables are considered with the Neumann boundary-value conditions. Sufficient conditions of the Andronov–Hopf bifurcation of periodic solutions are obtained along with expansions of the solutions in powers of small parameter. Spectral properties of the linearized elliptic operator of this problem are investigated. Necessary and sufficient conditions of normality are obtained for such operators. Examples on their properties are given.

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English version:
Journal of Mathematical Sciences, 2008, 153:5, 649–682

Bibliographic databases:

UDC: 517.956.4

Citation: E. M. Varfolomeev, “On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics”, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), CMFD, 21, PFUR, M., 2007, 5–36; Journal of Mathematical Sciences, 153:5 (2008), 649–682

Citation in format AMSBIB
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\by E.~M.~Varfolomeev
\paper On some properties of elliptic and parabolic functional differential operators arising in nonlinear optics
\inbook Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A.~L.~Skubachevskii (Peoples' Friendship University of Russia)
\serial CMFD
\yr 2007
\vol 21
\pages 5--36
\publ PFUR
\publaddr M.
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2336489}
\zmath{https://zbmath.org/?q=an:1157.35116}
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\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 153
\issue 5
\pages 649--682
\crossref{https://doi.org/10.1007/s10958-008-9141-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-54249154548}


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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. M. Selitskii, “Modelirovanie nekotorykh opticheskikh sistem na osnove parabolicheskogo differentsialno-raznostnogo uravneniya”, Matem. modelirovanie, 24:12 (2012), 38–42  mathnet  mathscinet
    2. A. B. Muravnik, “Functional differential parabolic equations: integral transformations and qualitative properties of solutions of the Cauchy problem”, Journal of Mathematical Sciences, 216:3 (2016), 345–496  mathnet  crossref
    3. A. L. Skubachevskii, “Boundary-value problems for elliptic functional-differential equations and their applications”, Russian Math. Surveys, 71:5 (2016), 801–906  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Muravnik A., “On the Half-Plane Dirichlet Problem For Differential-Difference Elliptic Equations With Several Nonlocal Terms”, Math. Model. Nat. Phenom., 12:6, SI (2017), 130–143  crossref  mathscinet  zmath  isi  scopus
    5. Tasevich A., “Analysis of Functional-Differential Equation With Orthotropic Contractions”, Math. Model. Nat. Phenom., 12:6, SI (2017), 240–248  crossref  mathscinet  zmath  isi  scopus
    6. V. A. Popov, “Otsenki reshenii ellipticheskikh differentsialno-raznostnykh uravnenii s vyrozhdeniem”, Differentsialnye i funktsionalno-differentsialnye uravneniya, SMFN, 64, no. 1, Rossiiskii universitet druzhby narodov, M., 2018, 131–147  mathnet  crossref
    7. D. A. Neverova, “Gladkost obobschennykh reshenii vtoroi i tretei kraevykh zadach dlya silno ellipticheskikh differentsialno-raznostnykh uravnenii”, Trudy Matematicheskogo instituta im. S.M. Nikolskogo RUDN, SMFN, 65, no. 4, Rossiiskii universitet druzhby narodov, M., 2019, 655–671  mathnet  crossref
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