Author | Kuzin, I. author |
---|---|
Title | Entire Solutions of Semilinear Elliptic Equations [electronic resource] / by I. Kuzin, S. Pohozaev |
Imprint | Basel : Birkhรคuser Basel, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-9250-6 |
Descript | 260 p. online resource |
ยง 0 Notation -- 1 Classical Variational Method -- ยง 1 Preliminaries -- ยง 2 The Classical Method: Absolute Minimum -- ยง 3 Approximation by Bounded Domains -- ยง 4 Approximation for Problems on an Absolute Minimum -- ยง 5 The Monotonicity Method. Uniqueness of Solutions -- 2 Variational Methods for Eigenvalue Problems -- ยง 6 Abstract Theorems -- ยง 7 The Equation โ?u + a(X) ?2u ? ?b ?2u = 0 -- ยง 8 Radial Solutions โ?u + ?f(u) = 0 -- ยง 9 The Equation โ?u ? ? ?2u ? b ?2u = 0 -- ยง 10 The Equation -- ยง 11 The Comparison Method for Eigenvalue Problems (Concentration Compactness) -- ยง 12 Homogeneous Problems -- 3 Special Variational Methods -- ยง 13 The Mountain Pass Method -- ยง 14 Behavior of PS-sequences. The Concentration Compactness (Comparison) Method -- ยง 15 A General Comparison Theorem. The Ground State. Examples for the Mountain Pass Method -- ยง 16 Behavior of PS-sequences in the Symmetric Case. Existence Theorems -- ยง 17 Nonradial Solutions of Radial Equations -- ยง 18 Methods of Bounded Domains Approximation -- 4 Radial Solutions: The ODE Method -- ยง 19 Basic Techniques of the ODE Method -- ยง 20 Autonomous Equations in the N-dimensional Case -- ยง 21 Decaying Solutions. The One-dimensional Case -- ยง 22 The Phase Plane Method. The Emden-Fowler Equatio -- ยง 23 Scaling -- ยง 24 Positive Solutions. The Shooting Method -- 5 Other Methods -- ยง 25 The Method of Upper and Lower Solutions -- ยง 26 The Leray-Schauder Method -- ยง 27 The Method of A Priori Estimates -- ยง 28 The Fibering Method. Existence of Infinitely Many Solutions -- ยง 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