Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations

by Heikkila; Seppo

• ISBN13: 9780824792244
• ISBN10: 0824792246
• eBook ISBN(s): 9781351430159
• Format: Hardcover
• Copyright: 1994-05-02
• Publisher: CRC Press
• More Book Details

Summary

Presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations. DLC: Differential equations, Nonlinear-Numerical solutions.

Author Biography

Seppo Heikkila is an Associate Professor of Mathematics in the Faculty of Sciences and a Docent of Applied Mathematics in the Faculty of Technology at the University of Oulu, Finland.

Table of Contents

Preface	p. iii
Methods and Prerequisites	p. 1
Introduction	p. 1
Analysis in Ordered Spaces	p. 2
Fixed Point Theorems	p. 20
Ordered Normed and Function Spaces	p. 27
Results of Nonlinear Analysis	p. 36
Method of Upper and Lower Solutions	p. 67
Notes and Comments	p. 79
First Order Differential Equations	p. 83
Introduction	p. 83
Scalar Initial Value Problems	p. 85
Mixed Monotone IVP's	p. 107
First Order Periodic BVP's	p. 121
Finite Differential Systems	p. 134
Mixed Monotone Systems	p. 152
Periodic Boundary Value Systems	p. 164
Infinite Differential Systems	p. 175
Infinite Mixed Monotone Systems	p. 193
Infinite Systems of Periodic BVP's	p. 204
Notes and Comments	p. 216
Second Order Differential Equations	p. 217
Introduction	p. 217
Second Order BVP's	p. 218
Second Order Mixed Monotone BVP's	p. 233
Systems of Second Order BVP's	p. 240
Second Order Mixed Monotone BVP's	p. 255
Notes and Comments	p. 263
Second Order Partial Differential Equations	p. 265
Introduction	p. 265
Quasilinear Elliptic BVP's	p. 267
Elliptic Equations	p. 285
Elliptic Systems	p. 292
Parabolic IBVP's	p. 303
Parabolic Systems	p. 321
Notes and Comments	p. 327
Differential Equations in Banach Spaces	p. 329
Introduction	p. 329
Existence, Uniqueness & Extremality Results	p. 331
Extremal Solutions of Semilinear IVP's	p. 350
Higher Order Differential Equations	p. 366
Periodic Boundary Value Problems	p. 380
Mixed Monotone Equations	p. 394
On Mild Solutions of First Order IVP's	p. 415
Second Order Semilinear IVP's	p. 434
Ordered Banach & Function Spaces	p. 455
Notes and Comments	p. 486
References	p. 489
Index	p. 507
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