NONLINEAR UNCERTAIN SYSTEMS AND NECESSARY CONDITIONS OF OPTIMALITY

In this paper we consider an optimal control problem for a class of sy stems governed by nonlinear evolution equations containing a nonlinear monotone operator and a nonmonotone operator with uncertain parameter s. We prove existence of solutions and present necessary conditions of optimality. Our result is illustrated by an example from quasi-linear partial differential equations with uncertain coefficients. This resu lt is further illustrated by a more practical example.