This is an introduction to nonlinear functional analysis, in particular to those methods based on differential calculus in Banach spaces. It is in two parts; the first deals with the geometry of Banach spaces and includes a discussion of local and global inversion theorems for differentiable mappings. In the second part, the authors are more concerned with bifurcation theory, including the Hopf bifurcation. They include plenty of motivational and illustrative applications, which indeed provide much of the justification of nonlinear analysis. In particular, they discuss bifurcation problems...
This is an introduction to nonlinear functional analysis, in particular to those methods based on differential calculus in Banach spaces. It is in two...
Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a...
Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R...
Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A...
Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the i...
Contents: I. Ekeland: Some Variational Methods Arising from Mathematical Economics.- A. Mas-Colell: Four Lectures on the Differentiable Approach to General Equilibrium Theory.- J. Scheinkman: Dynamic General Equilibrium Models.- S. Zamir: Topics in Non Cooperative Game Theory.
Contents: I. Ekeland: Some Variational Methods Arising from Mathematical Economics.- A. Mas-Colell: Four Lectures on the Differentiable Approach to Ge...
This self-contained textbook provides the basic, abstracttoolsused innonlinear analysisand their applications to semilinear elliptic boundary value problems and displays how variousapproachescan easily beappliedto a range of model cases.
Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is apractical text for an introductory course or seminar on nonlinear functional analysis."
This self-contained textbook provides the basic, abstracttoolsused innonlinear analysisand their applications to semilinear elliptic boundary value...
Le equazioni differenziali sono un argomento fondamentale non solo della matematica, ma anche della fisica, dell'ingegneria e, in generale, di tutte le scienze. Questo volume intende fornire allo studente una panoramica di alcune tra le piu interessanti e suggestive questioni relative alle equazioni differenziali ordinarie trattate da un punto di vista geometrico, aprendo uno sguardo verso l'analisi funzionale. Oltre ai risultati classici sulle equazioni lineari, molto spazio e dato ai problemi nonlineari che spesso non sono oggetto dei corsi istituzionali.
L'esposizione e tenuta a un...
Le equazioni differenziali sono un argomento fondamentale non solo della matematica, ma anche della fisica, dell'ingegneria e, in generale, di tutt...
This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the...
This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rig...
