Entire Solutions of Semilinear Elliptic Equations

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