Symmetry-breaking bifurcation for the one-dimensional Liouville type equation
Satoshi Tanaka
TL;DR
This paper investigates the symmetry-breaking bifurcation in solutions to a one-dimensional Liouville type boundary value problem, utilizing Morse index techniques to establish new bifurcation results.
Contribution
It introduces a novel approach to analyze symmetry-breaking bifurcations in Liouville equations using Morse index, advancing understanding of solution structures.
Findings
Established symmetry-breaking bifurcation results.
Applied Morse index to analyze solution stability.
Identified conditions for bifurcation occurrence.
Abstract
The two-point boundary value problem for the one-dimensional Liouville type equation is considered. In this paper, a symmetry-breaking result is obtained by using the Morse index.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Stability and Controllability of Differential Equations · Advanced Mathematical Modeling in Engineering