An Existence Theorem for General Control Problems of Nonlinear Evolution Equations of First Order

Abstract

An existence theorem for the solution of optimal control problems of systems governed by the state equation $y+vAy+B(y)=u$ is proved, where $A$ is a linear operator and $B$ a nonlinear operator with $||B(y)|{|}_n\le c(1+||y|{|}_m^r)$.