Geodesic
The principle of limit amplitude
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 24 (1969) no. 3, pp. 97-167

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The paper deals with the asymptotic behaviour (as $t\to\infty$) of the solutions of some non-stationary problems in mathematical physics. The main aim of the paper is to clarify conditions under which stationary oscillations can be obtained from non-stationary ones in the limit $t\to\infty$. We study the case of an elliptic self-adjoint second order operator acting in an infinite domain with a finite boundary. We also discuss some higher order operators, as well as the Laplace operator in a domain of special type with an infinite boundary. 
@article{RM_1969_24_3_a2,
     author = {D. M. \`Eidus},
     title = {The principle of limit amplitude},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {97--167},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1969_24_3_a2/}
}
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D. M. Èidus. The principle of limit amplitude. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 24 (1969) no. 3, pp. 97-167. http://geodesic.mathdoc.fr/item/RM_1969_24_3_a2/