Existence results for some higher-order evolution equations with operator coefficients

摘要

In this paper we study and obtain the existence of C(r)-pseudo almost automorphic solutions to some higher-order differential equations with operator coefficients whose forcing is C(s)-pseudo almost automorphic. We next use these abstract results to study the existence of C(r)-pseudo almost automorphic solutions to some second-order differential equations in Hilbert space which, among other things, model the so-called linear beam equation.