First and second order optimality conditions for optimal control   problems of state constrained integral equations
  This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions. 
J. Fr\'ed\'eric Bonnans (CMAP, INRIA Saclay - Ile de France),   Constanza De La Vega (DM-UBA, CONICET), Xavier Dupuis (CMAP,...
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