We consider the well-posedness of the second-order degenerate differential equations with infinite delay : , with periodic boundary conditions , , in Lebesgue–Bochner spaces and periodic Besov spaces , where , , and are closed linear operators in a Banach space satisfying , and . We completely characterize the well-posedness of in the above function spaces by using known operator-valued Fourier multiplier theorems. We also give concrete examples to support our abstract results.
"Solutions of second-order degenerate equations with infinite delay in Banach spaces." J. Integral Equations Applications 32 (3) 259 - 274, Fall 2020. https://doi.org/10.1216/jie.2020.32.259