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Boundary Conditions in Variational Problems

Chapter
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Abstract

As we have seen in chapter 2, the solution of the problem of finding an extremum of the functional
$$J(x) = \int\limits_0^T {f(x,\dot x,t)dt} $$
(1)
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.

Keywords

Marginal Cost Euler Equation Marginal Utility Order Differential Equation Transversality Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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