Bounded solutions, almost periodic in time, of a class of nonlinear evolution equations

An evolution equation of the form $u'+L(t)u+A(t)u=f$ is considered, where $L(t)$ is a linear maximally monotone (unbounded) operator and $A(t)$ a nonlinear bounded monotone operator that satisfies a coerciveness condition. Existence theorems are established for bounded and almost periodic (in the senses of Stepanov, Bohr, and Besicovitch) solutions. The theory is then applied to symmetric hyperbolic systems and to some nonlinear Schrödinger-type equations.
Bibliography: 19 titles.