PERIODIC AND ALMOST PERIODIC COSINE OPERATOR FUNCTIONS
Sergey Igorevich Piskarev · Mathematics of the USSR-Sbornik · 1983
Necessary and sufficient conditions are established for a well-posed Cauchy problem to have an almost periodic (periodic) solution in a Banach space. The influence of how "scattered" the spectrum is on almost-periodicity of a cosine operator function giving the solution of (1) is determined. Results relating to the Cauchy problem for the nonhomogeneous equation are presented. Bibliography: 29 titles.