This is a nicely organized introduction to the direct methods of variational calculus focusing on the study of critical points of nonlinear functionals. It addresses students of mathematics and physics, and gives many applications to mechanics, classical field theory, boundary and eigenvalue problems of important partial differential equations, and also modern Thomas-Fermi theory.

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Variational Methods in Mathematical Physics This textbook is a comprehensive introduction to variational methods. Its unifying aspect, based on appropriate concepts of compactness, is the study of critical points of functionals via direct methods. It shows the interactions between linear and nonlinear functional analysis. Addressing in particular the interests of physicists, the authors treat in detail the variational problems of mechanics and classical field theories, writing on local linear and nonlinear boundary and eigenvalue problems of important classes of nonlinear partial differential equations, and giving more recent results on Thomas-Fermi theory and on problems involving critical nonlinear...

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