Ilya A. Kuzin, Stanislav I. Pohozaev

Entire Solutions of Semilinear Elliptic Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Basel
• Seitenzahl: 260
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034892506
• Artikelnr.: 53316678

Inhaltsangabe

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.