Pseudo-almost periodic and pseudo-almost automorphic solutions to evolution equations in Hilbert spaces (Q277020)

The paper deals with the differential equation \[ \frac{du}{dt}(t)=Au(t)+Bu(t)+F(t,u(h(t))),\quad t\in\mathbb{R},\tag{1} \] where \(A\), \(B\) are densely defined closed linear operators on a Hilbert space \(\mathbb{H}\), and \(F\), \(h\) are appropriate functions which satisfy some assumptions. By using some composition theorems combined with the Banach contraction mapping principle and the method of invariant subspaces for unbounded linear operators, the authors prove the existence and uniqueness of \(\mu\)-pseudo-almost periodic and \(\mu\)-pseudo-almost automorphic solutions of equation (1).