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We obtain an existence-uniqueness result for
a second order Neumann boundary value problem including cases
where the nonlinearity possibly crosses several points of
resonance. Optimal and Schauder fixed points methods are used to
prove this kind of results.
An optimal control for a nonlinear system is considered. The existence of an optimal-control pair, the characterization of the optimal control in terms of the optimal system and the uniqueness of solutions for the control problem are established. The uniqueness requires smallness assumptions on parameters in the functional.
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