The principle of limit amplitude

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.