# Two-mode bifurcation in solution of a perturbed nonlinear fourth order differential equation

Ahmed Abbas Mizeal; Mudhir A. Abdul Hussain

Archivum Mathematicum (2012)

- Volume: 048, Issue: 1, page 27-37
- ISSN: 0044-8753

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topMizeal, Ahmed Abbas, and Hussain, Mudhir A. Abdul. "Two-mode bifurcation in solution of a perturbed nonlinear fourth order differential equation." Archivum Mathematicum 048.1 (2012): 27-37. <http://eudml.org/doc/246547>.

@article{Mizeal2012,

abstract = {In this paper, we are interested in the study of bifurcation solutions of nonlinear wave equation of elastic beams located on elastic foundations with small perturbation by using local method of Lyapunov-Schmidt.We showed that the bifurcation equation corresponding to the elastic beams equation is given by the nonlinear system of two equations. Also, we found the parameters equation of the Discriminant set of the specified problem as well as the bifurcation diagram.},

author = {Mizeal, Ahmed Abbas, Hussain, Mudhir A. Abdul},

journal = {Archivum Mathematicum},

keywords = {bifurcation theory; nonlinear systems; local Lyapunov-Schmidt method; bifurcation theory; nonlinear system; local Lyapunov-Schmidt method},

language = {eng},

number = {1},

pages = {27-37},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Two-mode bifurcation in solution of a perturbed nonlinear fourth order differential equation},

url = {http://eudml.org/doc/246547},

volume = {048},

year = {2012},

}

TY - JOUR

AU - Mizeal, Ahmed Abbas

AU - Hussain, Mudhir A. Abdul

TI - Two-mode bifurcation in solution of a perturbed nonlinear fourth order differential equation

JO - Archivum Mathematicum

PY - 2012

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 048

IS - 1

SP - 27

EP - 37

AB - In this paper, we are interested in the study of bifurcation solutions of nonlinear wave equation of elastic beams located on elastic foundations with small perturbation by using local method of Lyapunov-Schmidt.We showed that the bifurcation equation corresponding to the elastic beams equation is given by the nonlinear system of two equations. Also, we found the parameters equation of the Discriminant set of the specified problem as well as the bifurcation diagram.

LA - eng

KW - bifurcation theory; nonlinear systems; local Lyapunov-Schmidt method; bifurcation theory; nonlinear system; local Lyapunov-Schmidt method

UR - http://eudml.org/doc/246547

ER -

## References

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