Bifurcation of Fredholm Maps II; The Dimension of the Set of Bifurcation Points
Jacobo Pejsachowicz
TL;DR
This paper provides an estimate for the dimension of the set of bifurcation points in nonlinear elliptic boundary value problems, based on the principal symbol of the linearized problem.
Contribution
It introduces a method to estimate the dimension of bifurcation point sets using the principal symbol of the linearization, advancing understanding of bifurcation structures.
Findings
Estimate for the covering dimension of bifurcation points set
Relation between bifurcation points and principal symbol
Application to nonlinear elliptic boundary value problems
Abstract
We obtain an estimate for the covering dimension of the set of bifurcation points for solutions of nonlinear elliptic boundary value problems from the principal symbol of the linearization of the problem along the trivial branch of solutions.
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Taxonomy
TopicsDifferential Equations and Boundary Problems · Nonlinear Differential Equations Analysis · Differential Equations and Numerical Methods