Periodic L 2 -Solutions of an Integrodifferential Equation in a Hilbert Space

Olof J. Staffans
1993 Proceedings of the American Mathematical Society  
Let A be a closed, densely defined operator in a Hilbert space X , and let p , v , and n be finite, scalar-valued measures on R. Consider the abstract integrodifferential equation where / is a 27t-periodic L2 function with values in X . We give necessary and sufficient conditions for this equation to have a mild 2^-periodic L2-solution with values in X for all /, as well as necessary and sufiicient conditions for it to have a strong solution for all f. Furthermore, we give necessary and
more » ... cessary and sufficient conditions for the operator mapping / into the periodic solution u to be compact. These results are applied to prove existence of periodic solutions of a nonlinear equation.
doi:10.2307/2159137 fatcat:bekqhocidvba7l25roskhsrvwi