On necessary optimality conditions for systems governed by a two point boundary value problem. II

Abstract

The present paper is a free continuation of [6] and deals with a control problem for a quasilinear second order ordinary differential equation with homogeneous Dirichlet boundary conditions. The control function occurs in all coefficients of the differential equation and its values are supposed to be elements of a given arbitrary set Q ⊂ R m Using needle-like variation of the optimal control and via a suitable representation of the related state a necessary Pontryagin like optimality condition is derived.