Comparison method of partial functional-differential equations and its application. (Q1855127)

Here, the initial value problem \[ \frac{du}{dt} = Au + f(t,u_t), \quad t \geq 0, \qquad u = \varphi (t), \quad t \in [-r,0], \] is considered on the real Banach space \(X\), where \(u_t = u(t + \theta)\), \(-r \leq \theta \leq 0\), and \(A\) is a linear operator on \(X\). The authors discuss the existence of local and global solutions and study the stability of the trivial solution. The results are applied to a neutron reactor model with time delay.