Entire Solutions of Semilinear Elliptic Equations

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.