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 Mat. Sb. (N.S.), 1971, Volume 86(128), Number 1(9), Pages 90–109 (Mi msb3285)

On the principle of limiting amplitude

B. R. Vainberg

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.

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English version:
Mathematics of the USSR-Sbornik, 1971, 15:1, 89–108

Bibliographic databases:

UDC: 517.946.6
MSC: Primary 35J30; Secondary 35J05

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/msb3285} \mathscinet{http://www.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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This publication is cited in the following articles:
1. B. R. Vainberg, “On exterior elliptic problems polynomially depending on a spectral parameter, and the asymptotic behavior for large time of solutions of nonstationary problems”, Math. USSR-Sb., 21:2 (1973), 221–239
2. B. R. Vainberg, “On the short wave asymptotic behaviour of solutions of stationary problems and the asymptotic behaviour as $t\to\infty$ of solutions of non-stationary problems”, Russian Math. Surveys, 30:2 (1975), 1–58
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