# Good reference for the construction of a Greens functions fur the Sturm-Liouville

Does anyone know a good reference for the constructions of a Greens functions fur the Sturm-Liouville Boundary Value Problem.

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

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:

• ODE
• PDE with initial conditions
• PDE with boundary conditions.

I found a preview here

Cheers

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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 :-)

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

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Levitan B.M., Sargsjan I.S. Sturm-Liouville and Dirac operators. Kluwer, 1991. xii+350 pp. ISBN: 0-7923-0992-8

Section I.5 of this book contains a detailed construction of Green's function for the Sturm-Liouville problem.

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My go-to book for all things Sturm-Liouville, including more modern stuff, is Zettl's Sturm-Liouville theory (AMS, 2005).

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