Second order necessary conditions for general problems with state inequality constraints

The paper is a sequel to an article by the author, concerned with a certain canonical problem in optimal control involving constraints of the type (Psi sup alpha) (t,x) or = 0 alpha = 1,...,m. In that article a set of second order conditions necessary for a solution arc was obtained. In the paper those results are extended to a general control problem involving the above type of constraints. (Author)