Variational methods: applications to nonlinear partial differential equations and hamiltonian systems

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radó. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The fourth edition gives a survey on new developments in the field. In particular it includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. Gives a concise introduction to the field of Variational Methods and presents an overview of areas of current research in this field. Valuable source of reference for advanced students and researchers in the currently very active field of variationalmethods. Includes the proof for the convergence of the Yamabe flow and a detailed treatment of the phenomenon of blow-up. INDICE: The Direct Methods in the Calculus of Variations.- Lower Semi-Continuity.- Constraints.- Compensated Compactness.- The Concentration-CompactnessPrinciple.- Ekeland's Variational Principle.- Duality.- Minimization ProblemsDepending on Parameters.- Minimax Methods.- The Finite Dimensional Case.- ThePalais-Smale Condition.- A General Deformation Lemma.- The Minimax Principle.- Index Theory.- The Mountain Pass Lemma and its Variants.- Perturbation Theory.- Linking.- Parameter Dependence.- Critical Points of Mountain Pass Type.- Non-Differentiable Functionals.- Ljusternik-Schnirelman Theory on Convex Sets.-Limit Cases of the Palais-Smale Condition.- Pohozaev's Non-Existence Result.-The Brezis-Nierenberg Result.- The Effect of Topology.- The Yamabe Problem.- The Dirichlet Problem for the Equation of Constant Mean Curvature.- Harmonic Maps of Riemannian Surfaces.- Appendix A.- Appendix B.- Appendix C.- References.- Index.

• ISBN: 978-3-540-74012-4
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 320
• Fecha Publicación: 01/01/2008
• Nº Volúmenes: 1
• Idioma: Inglés