Description

1. Find the extremal of the functional

subject to the boundary conditions y(0) = 1,y(1) = 0,z(0) = 0,z(1) = e.
2. Find the extremal of the functional

3. Find the extremal of the functional

subject to the boundary conditions
4. Find the extremal of the functional

How many boundary conditions do you need to specify at the two endpoints to determine the extremal uniquely?
5. Find the extremal of the functional

subject to the conditions y(0) = 0,y(1) = 0 and the constraint
6. Find the extremal of the functional