Mathematics for Economists

Calculus of variations

Example

Find

Z 1

0

r

1 +



x

 2

dt!min

x( 0 )= 0 ,x( 1 )= 1.

The kernel function is

F



t,x,x



=

r

1 +



x

 2

The EulerñLagrange equation is

0 =

d

dt

1

2

r^1

1 +



x

 22

x