Theory of Branching of Solutions of Non-Linear Equations (M. M. Vainberg and V. A. Trenogin)

Laetsch, Theodore W.

doi:10.1137/1018033

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1976

2019

Publication Types

Select...

Article4

Book2

Relationship

Self Cite0

Independent6

Authors

Journals

Cited by 12 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Lyapunov-Schmidt method can reduce equation (1) to equation (2), in which equation (2) has all the analytical and topological features of equation (1) (bifurcation diagram, multiplicity, etc. ), as such information can be found in [7], [8], [9], [13]. Singularities of smooth maps play an important part in the investigation of bifurcation solutions of BVPs.…”

Section: Introductionmentioning

confidence: 99%

The Analysis of Bifurcation Solutions by Angular Singularities

Kadhim

Hussain

2019

Comm. Math. & Appl.

View full text Add to dashboard Cite

This paper studies a nonlinear wave equation's bifurcation solutions of elastic beams situated on elastic bases with small perturbation by using the local method of Lyapunov-Schmidt. We have found the Key function corresponding to the functional related to this equation. The bifurcation analysis of this function has been investigated by the angular singularities. We have found the parametric equation of the bifurcation set (caustic) with the geometric description of this caustic. Also, the critical points' bifurcation spreading has been found.

show abstract

Section: Introductionmentioning

confidence: 99%