Green's Functions and Boundary Value Problems
by Ivar Stakgold, Michael J. Holst · Wiley
The graduate reference on the subject. The canonical treatment of the Green's-function half of this topic, at the level where BVPs become operator theory. Stakgold and Holst develop distributions, one-dimensional boundary value problems, Hilbert space and operator theory, spectral theory of differential operators, nonlinear problems, and a long chapter on finite-element approximation and iterative solvers.
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