E-Book, Englisch, 286 Seiten, Web PDF
Guo / Lakshmikantham / Ames Nonlinear Problems in Abstract Cones
1. Auflage 2014
ISBN: 978-1-4832-6190-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 286 Seiten, Web PDF
ISBN: 978-1-4832-6190-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Notes and Reports in Mathematics in Science and Engineering, Volume 5: Nonlinear Problems in Abstract Cones presents the investigation of nonlinear problems in abstract cones. This book uses the theory of cones coupled with the fixed point index to investigate positive fixed points of various classes of nonlinear operators. Organized into four chapters, this volume begins with an overview of the fundamental properties of cones coupled with the fixed point index. This text then employs the fixed point theory developed to discuss positive solutions of nonlinear integral equations. Other chapters consider several examples from integral and differential equations to illustrate the abstract results. This book discusses as well the fixed points of increasing and decreasing operators. The final chapter deals with the development of the theory of nonlinear differential equations in cones. This book is a valuable resource for graduate students in mathematics. Mathematicians and researchers will also find this book useful.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Nonlinear Problems in Abstract Cones;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;8
6;CHAPTER 1. BASIC PROPERTIES OF CONES;10
6.1;1.0 Introduction;10
6.2;1.1 Normal Cones;10
6.3;1.2 Regular and Fully Regular Cones;15
6.4;1.3 Minihedral and Strongly Minihedral Cones;22
6.5;1.4 Positive Linear Functionals;26
6.6;1.5 The e-Norm and Hilbert's Projective Metric;35
6.7;1.6 Notes and Comments;45
7;CHAPTER 2. POSITIVE FIXED POINT THEORY;48
7.1;2.0 Introduction;48
7.2;2.1 Fixed Points of Monotone Operators;49
7.3;2.2 Fixed Points of Concave and Convex Operators;68
7.4;2.3 Fixed Points .f Cone Expansion and Compression;91
7.5;2.4 Multiple Fixed Point Theorems;121
7.6;2.5 Fixed Points of domain Expansion and Compression;135
7.7;2.6 Notes and Comments;145
8;CHAPTER 3. APPLICATIONS TO NONLINEAR INTEGRAL EQUATIONS;147
8.1;3.0 Introduction;147
8.2;3.1 Integral Equations of Polynomial Type;147
8.3;3.2 Eigenvalues and Eigenfunctions;165
8.4;3.3 Some Nonlinear Integral Equations Arising in Science;178
8.5;3.4 Infinitely Many Solutions Obtained by Variational Methods;205
8.6;3.5 Notes and Comments;225
9;CHAPTER 4. APPLICATIONS TO NONLINEAR DIFFERENTIAL EQUATIONS;227
9.1;4.0 Introduction;227
9.2;4.1 Differential Inequalities;227
9.3;4.2 Flow-Invariant Sets;235
9.4;4.3 Method of Upper and Lower Solutions;241
9.5;4.4 Monotone Iterative Technique;245
9.6;4.5 Method of Upper and Lower Quasi-solutions;253
9.7;4.6 Cone-valued Lyapunov Functions and Stability Theory;258
9.8;4.7 Notes and Comments;265
10;APPENDIX;266
10.1;A.1 Separation Theorems of Convex Sets;266
10.2;A.2 Zorn's Lemma;266
10.3;A.3 Leray-Schauder Degree;267
10.4;A.4 Properties of Nemitskii Operators;274
10.5;A.5 Extension Theorems;275
11;REFERENCES;276
