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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 4, Pages 782–809 (Mi izv1647)  

This article is cited in 2 scientific papers (total in 2 papers)

Representations of solutions of periodic partial differential equations

P. A. Kuchment


Abstract: A variant of the Floquet theory for partial differential equations is constructed. Exponentially increasing solutions of periodic hypoelliptic equations and systems are decomposed into integrals over Floquet solutions. Analogous results are obtained for equations with deviating argument and for boundary-value problems in domains of the periodic wave guide type. The question of nonzero $L_2(\mathbf R^n)$-solutions of equations in these classes is also examined.
Bibliography: 41 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1983, 21:1, 93–117

Bibliographic databases:

UDC: 517.9
MSC: Primary 35C15, 35H05; Secondary 32C35, 32E10, 32L05, 32L10, 35B05, 35J55, 35R10, 4
Received: 12.06.1979

Citation: P. A. Kuchment, “Representations of solutions of periodic partial differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 46:4 (1982), 782–809; Math. USSR-Izv., 21:1 (1983), 93–117

Citation in format AMSBIB
\Bibitem{Kuc82}
\by P.~A.~Kuchment
\paper Representations of solutions of periodic partial differential equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 4
\pages 782--809
\mathnet{http://mi.mathnet.ru/izv1647}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=670166}
\zmath{https://zbmath.org/?q=an:0509.35006|0529.35009}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 1
\pages 93--117
\crossref{https://doi.org/10.1070/IM1983v021n01ABEH001642}


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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. P. A. Kuchment, “Floquet theory for partial differential equations”, Russian Math. Surveys, 37:4 (1982), 1–60  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. P. A. Kuchment, “Spherical representation of solutions of invariant differential equations on a Riemannian symmetric space of noncompact type”, Math. USSR-Izv., 27:3 (1986), 535–548  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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