Abstract
Existence, uniqueness and continuous dependence theorems for a class of third-order differential equations with anti-periodic boundary conditions are given. Applications to optimal control of the deflection of a three-layer beam are also given. The methods used here are: the Leray-Schauder′s continuation theorem, the Wirtinger-Poincaré type inequalities, the monotonicity method (maximal monotone operators) and the penalizations (of convex functionals) of Barbu′s type.
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