Overview

Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. This book presents a wealth of modern methods to solve such equations.Readers of this exposition will be advanced students and researchers in mathematics, physics and other.

Full Product Details

Author:   Ilya A. Kuzin ,  Stanislav I. Pohozaev
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   1997 ed.
Volume:   33
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   1.200kg
ISBN:  

9783764353230

ISBN 10:   3764353236
Pages:   260
Publication Date:   23 September 1997
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

§ 0 Notation.- 1 Classical Variational Method.- § 1 Preliminaries.- § 2 The Classical Method: Absolute Minimum.- § 3 Approximation by Bounded Domains.- § 4 Approximation for Problems on an Absolute Minimum.- § 5 The Monotonicity Method. Uniqueness of Solutions.- 2 Variational Methods for Eigenvalue Problems.- § 6 Abstract Theorems.- § 7 The Equation —?u + a(X) |u|p?2u ? ?b|u|q?2u = 0.- § 8 Radial Solutions —?u + ?f(u) = 0.- § 9 The Equation —?u ? ?|u|p?2u ? b|u|q?2u = 0.- § 10 The Equation.- § 11 The Comparison Method for Eigenvalue Problems (Concentration Compactness).- § 12 Homogeneous Problems.- 3 Special Variational Methods.- § 13 The Mountain Pass Method.- § 14 Behavior of PS-sequences. The Concentration Compactness (Comparison) Method.- § 15 A General Comparison Theorem. The Ground State. Examples for the Mountain Pass Method.- § 16 Behavior of PS-sequences in the Symmetric Case. Existence Theorems.- § 17 Nonradial Solutions of Radial Equations.- § 18 Methods of Bounded Domains Approximation.- 4 Radial Solutions: The ODE Method.- § 19 Basic Techniques of the ODE Method.- § 20 Autonomous Equations in the N-dimensional Case.- § 21 Decaying Solutions. The One-dimensional Case.- § 22 The Phase Plane Method. The Emden-Fowler Equatio.- § 23 Scaling.- § 24 Positive Solutions. The Shooting Method.- 5 Other Methods.- § 25 The Method of Upper and Lower Solutions.- § 26 The Leray-Schauder Method.- § 27 The Method of A Priori Estimates.- § 28 The Fibering Method. Existence of Infinitely Many Solutions.- § 29 Nonexistence Results.- Appendices.- A Spaces and Functionals.- B The Strauss Lemma.- C Invariant Spaces.- D The Schwarz Rearrangement.- E The Mountain Pass Method.- References.

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