Well‐posedness of second order degenerate integro‐differential equations with infinite delay in vector‐valued function spaces
Gang Cai, Shangquan Bu · Mathematische Nachrichten · 2015
We study the well‐posedness of the second order degenerate differential equations with infinite delay: with periodic boundary conditions , where and M are closed linear operators in a Banach space satisfying , . Using operator‐valued Fourier multiplier techniques, we give necessary and sufficient conditions for the well‐posedness of this problem in Lebesgue‐Bochner spaces , periodic Besov spaces and periodic Triebel‐Lizorkin spaces .