Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate

摘要: Abstract Problems are studied in which an integral of the form ∫ 0 +∞ L ( k t ), )) e − pt dt is minimized over a class arcs : [0, +∞) → R n . It assumed that convex function on × and discount rate ϱ positive. Optimality conditions expressed terms perturbed Hamiltonian differential system involving H , q ) concave but not necessarily differentiable. Conditions given ensuring that, for sufficiently small, has stationary point, neighborhood one classical “saddle point” behavior. The optimal interest then correspond to solutions tend point as +∞. These results motivated by questions theoretical economics extend previous work author case = 0.