Entire Solutions of Semilinear Elliptic Equations [Paperback]

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.

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 for radial solutions and the fibring method. Existence results for equations with supercritical growth and non-zero right-hand sides are given.
Readers of this exposition will be advanced students and researchers in mathematics, physics and other sciences who want to learn about specific methods to tackle problems involving 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 Dl3K