An Introduction to Nonlinear Functional Analysis and Elliptic Problems

This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems. By first outlining the advantages and disadvantages of each method, this comprehensive text displays how various approaches can easily be ...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριοι συγγραφείς: Ambrosetti, Antonio (Συγγραφέας), Arcoya, David (Συγγραφέας)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Boston : Birkhäuser Boston, 2011.
Σειρά:Progress in Nonlinear Differential Equations and Their Applications ; 82
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
LEADER 03390nam a22005055i 4500
001 978-0-8176-8114-2
003 DE-He213
005 20151103121020.0
007 cr nn 008mamaa
008 110720s2011 xxu| s |||| 0|eng d
020 |a 9780817681142  |9 978-0-8176-8114-2 
024 7 |a 10.1007/978-0-8176-8114-2  |2 doi 
040 |d GrThAP 
050 4 |a QA319-329.9 
072 7 |a PBKF  |2 bicssc 
072 7 |a MAT037000  |2 bisacsh 
082 0 4 |a 515.7  |2 23 
100 1 |a Ambrosetti, Antonio.  |e author. 
245 1 3 |a An Introduction to Nonlinear Functional Analysis and Elliptic Problems  |h [electronic resource] /  |c by Antonio Ambrosetti, David Arcoya. 
264 1 |a Boston :  |b Birkhäuser Boston,  |c 2011. 
300 |a XII, 199 p. 12 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Progress in Nonlinear Differential Equations and Their Applications ;  |v 82 
505 0 |a Notation -- Preliminaries -- Some Fixed Point Theorems -- Local and Global Inversion Theorems -- Leray-Schauder Topological Degree -- An Outline of Critical Points -- Bifurcation Theory -- Elliptic Problems and Functional Analysis -- Problems with A Priori Bounds -- Asymptotically Linear Problems -- Asymmetric Nonlinearities -- Superlinear Problems -- Quasilinear Problems -- Stationary States of Evolution Equations -- Appendix A Sobolev Spaces -- Exercises -- Index -- Bibliography. 
520 |a This self-contained textbook provides the basic, abstract tools used in nonlinear analysis and their applications to semilinear elliptic boundary value problems. By first outlining the advantages and disadvantages of each method, this comprehensive text displays how various approaches can easily be applied to a range of model cases. An Introduction to Nonlinear Functional Analysis and Elliptic Problems is divided into two parts: the first discusses key results such as the Banach contraction principle, a fixed point theorem for increasing operators, local and global inversion theory, Leray–Schauder degree, critical point theory, and bifurcation theory; the second part shows how these abstract results apply to Dirichlet elliptic boundary value problems.  The exposition is driven by numerous prototype problems and exposes a variety of approaches to solving them. Complete with a preliminary chapter, an appendix that includes further results on weak derivatives, and chapter-by-chapter exercises, this book is a practical text for an introductory course or seminar on nonlinear functional analysis. 
650 0 |a Mathematics. 
650 0 |a Dynamics. 
650 0 |a Ergodic theory. 
650 0 |a Functional analysis. 
650 0 |a Partial differential equations. 
650 1 4 |a Mathematics. 
650 2 4 |a Functional Analysis. 
650 2 4 |a Partial Differential Equations. 
650 2 4 |a Dynamical Systems and Ergodic Theory. 
700 1 |a Arcoya, David.  |e author. 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer eBooks 
776 0 8 |i Printed edition:  |z 9780817681135 
830 0 |a Progress in Nonlinear Differential Equations and Their Applications ;  |v 82 
856 4 0 |u http://dx.doi.org/10.1007/978-0-8176-8114-2  |z Full Text via HEAL-Link 
912 |a ZDB-2-SMA 
950 |a Mathematics and Statistics (Springer-11649)