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 nonlinearities. This book is an  excellentintroduction for students in mathematics and  mathematical physics.

Variational Methods in Mathematical Physics (Texts and Monographs in Physics) PDF

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