Boundary Conditions in Variational Problems



As we have seen in chapter 2, the solution of the problem of finding an extremum of the functional
$$J(x) = \int\limits_0^T {f(x,\dot x,t)dt} $$
amounts to solving the Euler equation \({f_x} - \frac{d}{{dt}}{f_{\dot x}} = 0\) . Since this is generally a second order differential equation, its solution involves two arbitrary constants which are determined by boundary conditions. These differ from problem to problem. They will now be discussed, starting from the simplest case of two fixed end points.


Marginal Cost Euler Equation Marginal Utility Order Differential Equation Transversality Condition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  1. 1.Department of EconomicsThe University of CalgaryN. W. CalgaryCanada

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