Stability and asymptotic behavior of solutions for some linear partial functional differential equations in critical cases (Q1015836)

The authors study the stability and the asymptotic behavior of the solution semigroup associated with the partial functional differential equation with infinite delay \[ \begin{cases} \frac{du}{dt}=Au\left( t\right) +L\left( u_{t}\right) ,\;t\geq0\\ u_{0}=\varphi \end{cases} \] where \(A\) is a closed linear operator on a Banach space, \(A\) satisfying the Hille-Yosida condition.