Maximal regularity of second-order equations with delay (Q2378191)

The author considers maximal regularity of the second-order differential equation with delay: \[ u''(t)+ Bu'(t)+ Au(t)= Gu_t'+ Fu_t+ f(t),\quad t\in\mathbb{R}, \] where \(A\) and \(B\) are closed linear operators defined on a Banach space \(X\), \(F\) and \(G\) are bounded linear operators and \(f\in C^\alpha(\mathbb{R}; X)\), \(0<\alpha< 1\). By the use of operator valued Fourier multipliers the existence and uniqueness of the solution is characterized. Moreover, maximal regularity of a particular equation, where \(A\) is sectorial, is considered.