Geodesic
On the principle of limiting amplitude
Sbornik. Mathematics, Tome 15 (1971) no. 1, pp. 89-108 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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B. R. Vainberg. On the principle of limiting amplitude. Sbornik. Mathematics, Tome 15 (1971) no. 1, pp. 89-108. http://geodesic.mathdoc.fr/item/SM_1971_15_1_a4/

[1] B. R. Vainberg, “Printsipy izlucheniya, predelnogo pogloscheniya i predelnoi amplitudy v obschei teorii uravnenii s chastnymi proizvodnymi”, Uspekhi matem. nauk, XXI:3(129) (1966), 115–194 | MR

[2] D. M. Eidus, “Printsip predelnoi amplitudy”, Uspekhi matem. nauk, XXIV:3(147) (1969), 91–156 | MR

[3] Psevdodifferentsialnye operatory (sb. statei), Mir, Moskva, 1967 | MR

[4] B. R. Vainberg, “Ob analiticheskikh svoistvakh rezolventy dlya odnogo klassa puchkov operatorov”, Matem. sb., 77(119) (1968), 259–296 | MR | Zbl

[5] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii i deistviya nad nimi, Fizmatgiz, Moskva, 1958 | Zbl

[6] B. R. Vainberg, “Povedenie resheniya zadachi Koshi dlya giperbolicheskogo uravneniya pri $t\to\infty$”, Matem. sb., 78(120) (1969), 542–578 | MR | Zbl