# American Institute of Mathematical Sciences

July  1995, 1(3): 371-388. doi: 10.3934/dcds.1995.1.371

## Optimality conditions for controls of semilinear evolution systems with mixed constraints

 1 Department of Mathematics, Fudan University, Shanghai 200433, China

Received  September 1994 Published  May 1995

In this paper, we study an optimal control problem for semilinear evolution equations with a mixed constraint of the state and the control. One of the motivations is the problem with a state dependent control domain. Our main result is the Pontryagin type necessary conditions for the optimal controls. The main tools we use are the Ekeland variational principle and the spike perturbation technique.
Citation: Jiongmin Yong. Optimality conditions for controls of semilinear evolution systems with mixed constraints. Discrete & Continuous Dynamical Systems - A, 1995, 1 (3) : 371-388. doi: 10.3934/dcds.1995.1.371
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