On a uniqueness theorem of L. Amerio and G. Prouse

Abstract

SynopsisWe give two generalizations of a theorem of L. Amerio and G. Prouse concerning uniqueness of the almost-periodic solution of the wave equation with a local multivalued damping term and almost-periodic forcing.Counterexamples are given which show that these results may fail if some hypotheses of the theorems are dropped. They also show that the two generalizations are relatively independent.