Nonlinear third-order differential equations with anti-periodic boundary conditions and some optimal control problems

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-Poincare type inequalities, the monotonicity method (maximal monotone operators) and the penalizations (of convex functionals) of Barbu′s type.