Please see the attached file for the fully formatted problems.
(a) FIND the Green's function for the operator with L = + w2 with u(a) = 0
dx2 u(b) = 0
and a < b, w2 a fixed constant. i.e. SOLVE Lu = ?ö(x ? ) with the given boundary conditions.
(b) Does this Green's function exist for all values of w? If NO, what are the exceptional values of w?
(c) Having found the Green's function in part (a), suppose one wishes to find the Green's function for the same differential equation, but with different end point
u(a)=0 . ,
conditions, namely , . How would one find this new Green s function u (a) = 0
using the work from part (a)? Find it.
The Green's function for an operator is found and discussed. The solution is detailed and well presented.