Entire Solutions of Semilinear Elliptic Equations

✍ Scribed by I. Kuzin, S. Pohozaev

• Publisher: Birkhäuser
• Year: 1997
• Tongue: English
• Leaves: 252
• Category: Library

✦ Table of Contents

Cover
Title page
Introduction
0 Notation
Chapter 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. U niqueness of Solutions
Chapter 2 Variational Methods for Eigenvalue Problems
6 Abstract Theorems
7 The Equation -Δu + a(x)|u|^{p-2}u - λb(x)|u|^{q-2}u = 0
8 Radial Solutions
9 The Equation -Δu + \lamdaf(u) = 0
10 The Equation -Δu - λ|u|^{p-2) u - b(x)|u|^{q-2}u = 0
11 The Comparison Method for Eigenvalue Problems (Concentration Compactness)
12 Homogeneous Problems
Chapter 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
Chapter 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 Equation
23 Scaling
24 Positive Solutions. The Shooting Method
Chapter 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
Index