Entire Solutions of Semilinear Elliptic Equations
Semilinear elliptic equations play an important role in many areas of mathematics and its applications to physics and other sciences. This book presents a wealth of modern methods to solve such equations, including the systematic use of the Pohozaev identities for the description of sharp estimates...
| Main Authors: | , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Basel
Birkhäuser
1997, 1997
|
| Edition: | 1st ed. 1997 |
| Series: | Progress in Nonlinear Differential Equations and Their Applications
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
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