Nonlinear Third-Order Differential Equations with Anti-periodic Boundary Conditions and Some Optimal Control Problems

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.