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

### Bernd Krause

Universität Leipzig, Germany

## 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 $||B(y)||_n ≤ c(1 + ||y||_m^r)$.

## Cite this article

Bernd Krause, An Existence Theorem for General Control Problems of Nonlinear Evolution Equations of First Order. Z. Anal. Anwend. 9 (1990), no. 2, pp. 113–120

DOI 10.4171/ZAA/386