Mathematics for Economists

Calculus of variations

Example

2 π

ZT

0

x(t)

r

1 +



x

 2

dt!min

x( 0 )=a,x(T)=b

The kernel is

F



t,x,x



=x

r

1 +



x

 2

The EulerñLagrange is

r

1 +



x

 2

= d

dt

r xx

1 +



x

 2