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Sufficient optimality conditions for multivariable control problems

Andrzej Nowakowski — 2007

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.

On the existence of multiple solutions for a nonlocal BVP with vector-valued response

Andrzej NowakowskiAleksandra Orpel — 2006

Czechoslovak Mathematical Journal

The existence of positive solutions for a nonlocal boundary-value problem with vector-valued response is investigated. We develop duality and variational principles for this problem. Our variational approach enables us to approximate solutions and give a measure of a duality gap between the primal and dual functional for minimizing sequences.

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