Low-dimensional qualitative and numerical approximation of bifurcation in a semilinear elliptic problem

DOI10.1016/0377-0427(87)90200-7zbMath0648.65077OpenAlexW2017551237MaRDI QIDQ1105332

Michael W. Smiley

Publication date: 1987

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(87)90200-7

zbMATH Keywords

numerical exampleseigenfunction expansionGalerkin approximationreduction processFourier series expansionnonlocal bifurcationseigenfunctions of the Laplace operator

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for linear elliptic equations (35J65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Bifurcations in context of PDEs (35B32)

Related Items

A numerical study of spontaneous bifurcation, A finite element method for computing the bifurcation function for semilinear elliptic BVPs, Approximation of the bifurcation function for elliptic boundary value problems, On the existence of smooth breathers for nonlinear wave equations

Uses Software

• PITCON

Cites Work

• S-shaped bifurcation curves of nonlinear elliptic boundary value problems
• Eigenfunction methods and nonlinear hyperbolic boundary value problems at resonance
• A numerical study of spontaneous bifurcation
• Global bifurcation of steady-state solutions
• Symmetry and related properties via the maximum principle
• On the number of solutions of a nonlinear Dirichlet problem
• On the Existence of Positive Solutions of Semilinear Elliptic Equations
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