Almost automorphic solutions for differential equations with piecewise constant argument in a Banach space (Q631704)

The author considers the differential equation with piecewise constant argument (EPCA) \[ x'(t)=A(t)x([t])+f(t), \] where \(A(t)\) is an \(X\)-valued 1-periodic operator and the forcing term is almost automorphic; \(X\) being a Banach space which does not contain any subspace isomorphic to \(c_0\). Using the concept of uniform spectrum due to Diagana-Minh-N'Guérékata combined with properties of almost automorphic sequences, the author proves that every bounded solution to (EPCA) is almost automorphic. The result generalizes a previous one by Nguyen Van Minh and Tran Dat in 2007.