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Mathematics of the USSR-Sbornik, 1971, Volume 15, Issue 1, Pages 89–108
DOI: https://doi.org/10.1070/SM1971v015n01ABEH001533 (Mi sm3285) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the principle of limiting amplitude

B. R. Vainberg
English version PDF (1030 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM1971v015n01ABEH001533
Abstract: In this paper we give a formulation and proof of a principle of limiting amplitude which allows one to select all of those solutions of the corresponding elliptic equation (of arbitrary order) which are obtained by means of the radiation conition and the principle of limiting absorption. In particular, the case when the latter two principles select more than two solutions is considered. The formulation of this new principle is connected with the transition to a certain nonstationary equation with several new variables, for which a Goursat-type problem is studied. The presence of several additional variables gives rise to a new resonance-like effect, which is also investigated.
Bibliography: 6 titles.
Received: 14.10.1970
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1971, Volume 86(128), Number 1(9), Pages 90–109
Bibliographic databases:
UDC: 517.946.6
MSC: Primary 35J30; Secondary 35J05
Language: English
Original paper language: Russian
Citation: B. R. Vainberg, “On the principle of limiting amplitude”, Mat. Sb. (N.S.), 86(128):1(9) (1971), 90–109; Math. USSR-Sb., 15:1 (1971), 89–108
Citation in format AMSBIB
\Bibitem{Vai71}
\by B.~R.~Vainberg
\paper On the principle of limiting amplitude
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 86(128)
\issue 1(9)
\pages 90--109
\mathnet{http://mi.mathnet.ru/sm3285}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=313658}
\zmath{https://zbmath.org/?q=an:0254.35036}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 15
\issue 1
\pages 89--108
\crossref{https://doi.org/10.1070/SM1971v015n01ABEH001533}
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  • https://www.mathnet.ru/eng/sm/v128/i1/p90
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
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    Abstract page:294
    Russian version PDF:117
    English version PDF:6
    References:49
     
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