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THE CALCULUS OF VARIATIONS
BOUNDARY CONDITIONS IN VARIATIONAL PROBLEMS
21 other sections not shown
arbitrary assumed assumption bang bang-bang bang-bang control bifurcation boundary conditions Calculus of Variations chapter Clearly coefficient concave constant consumption utility control variables convex cost curvature matrix curve defined determined differential equation differential game discussed dynamic system e~rt economic applications eigen values end points equilibrium point Euler equation gives example extremum fixed given Hamiltonian hence implies inequality constraints integration investment labour Liapunov function linear Linear Regulator marginal utility maximize the present Maximum Principle gives minimize minimum mixed strategies Nash equilibrium necessary conditions neo-classical Note objective functional obtained Optimal Control theory Optimal Growth Model output parameter payoff phase diagram player Pontryagin's positive definite present value production function resource Riccati equation saddle point satisfied scalar singular control solution solving Stackelberg strategies structural stability Substituting sufficient conditions switching function Theorem transversality conditions unspecified unstable utility function