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Global Solution Curves for Semilinear Elliptic Equations

Philip Korman
Publisher: 
World Scientific
Publication Date: 
2012
Number of Pages: 
241
Format: 
Hardcover
Price: 
90.00
ISBN: 
9789814374347
Category: 
Monograph
We do not plan to review this book.
  • Curves of Solutions on General Domains:
    • Continuation of Solutions
    • Symmetric Domains in R2
    • Turning Points and the Morse Index
    • Convex Domains in R2
    • Pohozaev's Identity and Non-Existence of Solutions for Elliptic Systems
    • Problems at Resonance
  • Curves of Solutions on Balls:
    • Preliminary Results
    • Positivity of Solution to the Linearized Problem
    • Uniqueness of the Solution Curve
    • Direction of a Turn and Exact Multiplicity
    • On a Class of Concave-Convex Equations
    • Monotone Separation of Graphs
    • The Case of Polynomial ƒ(u) in Two Dimensions
    • The Case When ƒ(0) < 0
    • Symmetry Breaking
    • Special Equations
    • Oscillations of the Solution Curve
    • Uniqueness for Non-Autonomous Problems
    • Exact Multiplicity for Non-Autonomous Problems
    • Numerical Computation of Solutions
    • Radial Solutions of Neumann Problem
    • Global Solution Curves for a Class of Elliptic Systems
    • The Case of a “Thin” Annulus
    • A Class of p-Laplace Problems
  • Two Point Boundary Value Problems:
    • Positive Solutions of Autonomous Problems
    • Direction of the Turn
    • Stability and Instability of Solutions
    • S-Shaped Solution Curves
    • Computing the Location and the Direction of Bifurcation
    • A Class of Symmetric Nonlinearities
    • General Nonlinearities
    • Infinitely Many Curves with Pitchfork Bifurcation
    • An Oscillatory Bifurcation from Zero: A Model Example
    • Exact Multiplicity for Hamiltonian Systems
    • Clamped Elastic Beam Equation
    • Steady States of Convective Equations
    • Quasilinear Boundary Value Problems
    • The Time Map for Quasilinear Equations
    • Uniqueness for a p-Laplace Case

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