A Topological Introduction to Nonlinear Analysis

• Κύριος συγγραφέας: Brown, Robert F. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2014.
• Έκδοση: 3rd ed. 2014.
• Θέματα: Mathematics.; Functional analysis.; Differential equations.; Partial differential equations.; Topology.; Functional Analysis.; Ordinary Differential Equations.; Partial Differential Equations.

This third edition of A Topological Introduction to Nonlinear Analysis is addressed to the mathematician or graduate student of mathematics - or even the well-prepared undergraduate - who would like, with a minimum of background and preparation, to understand some of the beautiful results at the hea...

Πίνακας περιεχομένων:

• Preface
• Part I Fixed Point Existence Theory
• The Topological Point of View
• Ascoli-Arzela Theory
• Brouwer Fixed Point Theory
• Schauder Fixed Point Theory
• The Forced Pendulum
• Equilibrium Heat Distribution
• Generalized Bernstain Theory
• Part II Degree Theory
• Brouwer Degree
• Properties of the Brouwer Degree
• Leray-Schauder Degree
• Properties of the Leray-Schauder Degree
• The Mawhin Operator
• The Pendulum Swings back
• Part III Fixed Point Index Theory
• A Retraction Theorum
• The Fixed Point Index
• The Tubulur Reactor
• Fixed Points in a Cone
• Eigenvalues and Eigenvectors
• Part IV Bifurcation Theory
• A Separation Theorem
• Compact Linear Operators
• The Degree Calculation
• The Krasnoselskii-Rabinowitz Theorem
• Nonlinear Strum Liouville Theory
• More Strum Liouville Theory
• Euler Buckling
• Part V Appendices.