A counter-example in the theory of almost periodic differential equations
It is known that if \(a(t)\) is a piecewise continuous periodic function, then any bounded solution of \(x''+ a(t) x= 0\) is almost periodic using Floquet theory. Is it still true if \(a(t)\) is merely almost periodic? The authors show by means of a counterexample to the statement that boundedness of a solution by itself implies almost periodicity. The result is also extended to linear differential equations of order \(k\).
scientific article; zbMATH DE number 796931