This textbook is a comprehensive introduction to variationalmethods. Its unifying aspect, based on appropriate conceptsof compactness, is the study of critical points offunctionals via direct methods. It shows the interactionsbetween linear and nonlinear functional analysis. Addressingin particular the interests of physicists, the authors treatin detail the variational problems of mechanics andclassical field theories, writing on local linear andnonlinear boundary and eigenvalue problems of importantclasses of nonlinear partial differential equations, andgiving more recent results on Thomas-Fermi theory and onproblems involving critical nonlinearities. This book is anexcellentintroduction for students in mathematics andmathematical physics.
