Description

Book Synopsis
This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented.The author is one of the original contributors to the field of exact multiplicity results.

Table of Contents
Continuation of Solutions in General Domain Curves of Positive Solutions on Balls; Symmetry Breaking; Curves with Infinitely Many Turns; Numerical Computation of Solutions; Solutions of Annular Domains Curves of Solutions to Hamiltonian Systems; S-Shapes Bifurcation Curves for Two Point Problems; Infinitely Many Solution Curves with Pitchfork Bifurcation; Elastic Beam Equations; Prescribed Mean Curvature Equation.

Global Solution Curves For Semilinear Elliptic

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    A Hardback by Philip Korman

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      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: Publication Date: 13/02/2012
      ISBN13: 9789814374347, 978-9814374347
      ISBN10: 9814374342

      Description

      Book Synopsis
      This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented.The author is one of the original contributors to the field of exact multiplicity results.

      Table of Contents
      Continuation of Solutions in General Domain Curves of Positive Solutions on Balls; Symmetry Breaking; Curves with Infinitely Many Turns; Numerical Computation of Solutions; Solutions of Annular Domains Curves of Solutions to Hamiltonian Systems; S-Shapes Bifurcation Curves for Two Point Problems; Infinitely Many Solution Curves with Pitchfork Bifurcation; Elastic Beam Equations; Prescribed Mean Curvature Equation.

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