On the periodic solutions of differential inclusions and applications (Q1890257)

The authors provide sufficient conditions for the existence of mild solutions for the following periodic problem of the nonlinear evolution inclusion \[ x'(t)\in Ax(t)+F(t,x(t))\quad \text{a.e. } t\in T=[0,b],\quad x(0)=x(b), \] where \(F:T\times X \to 2^{X}\) is a multivalued map and \(A:X\to X\) is an operator generating an equicontinuous semigroup of bounded linear operators \(T(t)\) in the separable Banach space \(X\). The proof relies on general multivalued analysis and Kakutani's fixed-point theorem. Some applications to periodic feedback control systems are considered, too.