On the principle of limiting amplitude

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.
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