Mathematics for Economists

Calculus of variations

Example

Study the problem with kernel

F



t,x,x



=x

r

1 +



x

 2

This a product of two convex functions.

det(HλI)=

(^)
(^)
(^)
(^)
λ x/
r
1 +



x

 2

x/

r

1 +



x

 2

x/



1 +



x

 2  3 / 2

λ

(^)
(^)
(^)
(^)