Does anyone know a good reference for the constructions of a Greens functions fur the SturmLiouville Boundary Value Problem.
My choice would be Boundary Value Problems and Green's Functions by Ivar Stakgold. It have an introduction to distribution theory and them apply it to finding Green's functions. It includes:
I found a preview here Cheers 


My favorite book on the subject is E. L. Ince, Ordinary differential equations. It is of originally of 1926, but it contains essentially everything what one has to know on the subject :) 


Courant, Hilbert, Methoden der mathematischen Physik (English version: Methods of Mathematical Physics). 


Levitan B.M., Sargsjan I.S. SturmLiouville and Dirac operators. Kluwer, 1991. xii+350 pp. ISBN: 0792309928 Section I.5 of this book contains a detailed construction of Green's function for the SturmLiouville problem. 


My goto book for all things SturmLiouville, including more modern stuff, is Zettl's SturmLiouville theory (AMS, 2005). 


references
tag should be added – Dox Aug 28 '12 at 11:37