On the Behavior of Solutions of the Cauchy Problem for a Hyperbolic Equation with Periodic Coefficients. The Principle of the Limiting Amplitude

This paper considers the Cauchy problem for a second-order hyperbolic equation with periodic coefficients and zero initial data, and the right-hand side of the equation is the function \(f(x)\,\exp\{-i\,\omega\,t\}\) , \(\omega>0\) . For this problem, the limiting amplitude principle and the asymptotic behavior as \(t\to\infty\) are established.