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Monotone iterative techniques for discontinuous nonlinear differential equations

Author: Heikkilä, Seppo ; Lakshmikantham, V. Series: Monographs and textbooks in pure and applied mathematics Publisher: Dekker, 1994.Language: EnglishDescription: 514 p. ; 24 cm.ISBN: 0824792246Type of document: BookBibliography/Index: Includes bibliographical references and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Europe Campus
Main Collection
Print QA372 .H45 1994
(Browse shelf)
001220791
Available 001220791
Total holds: 0

Includes bibliographical references and index

Digitized

Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations Contents Preface iii 1. METHODS AND PREREQUISITES 1.0. Introduction 1.1. Analysis in Ordered Spaces 1.2. Fixed Point Theorems 1.3. Ordered Normed and Function Spaces 1.4. Results of Nonlinear Analysis 1.5. Method of Upper and Lower Solutions 1.6. Notes and Comments 2. FIRST ORDER DIFFERENTIAL EQUATIONS 2.0. Introduction 2.1. Scalar Initial Value Problems 2.2. Mixed Monotone IVP's 2.3. First Order Periodic BVP's 2.4. Finite Differential Systems 2.5. Mixed Monotone Systems 1 1 2 20 27 36 67 79 83 83 85 107 121 134 152 vii viii Contents 2.6. Periodic Boundary Value Systems 2.7. Infinite Differential Systems 2.8. Infinite Mixed Monotone Systems 2.9. Infinite Systems of Periodic BVP's 2.10. Notes and Comments 164 175 193 204 216 3. SECOND ORDER DIFFERENTIAL EQUATIONS 3.0. Introduction 3.1. Second Order BVP's 3.2. Second Order Mixed Monotone BVP's 3.3. Systems of Second Order BVP's 3.4. Second Order Mixed Monotone BVP's 3.5. Notes and Comments 217 217 218 233 240 255 263 4. SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS 4.0. Introduction 4.1. Quasilinear Elliptic BVP's 4.2. Elliptic Equations 4.3. Elliptic Systems 4.4. Parabolic IBVP's 4.5. Parabolic Systems 4.6. Notes and Comments 265 265 267 285 292 303 321 327 5. DIFFERENTIAL EQUATIONS IN BANACH SPACES 5.0. Introduction 5.1. Existence, Uniqueness and Extremality Results 5.2. Extremal Solutions of Semilinear IVP's 5.3. Higher Order Differential Equations 5.4. Periodic Boundary Value Problems 5.5. Mixed Monotone Equations 329 329 331 350 366 380 394 Contents ix 5.6. On Mild Solutions of First Order IVP's 5.7. Second Order Semilinear IVP's 5.8. Ordered Banach and Function Spaces 5.9. Notes and Comments 415 434 455 486 489 507 References Index

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