Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation. (February 2018)

• Record Type: Journal Article
• Authors: Izydorek, Marek; Janczewska, Joanna; Waterstraat, Nils; Zgorzelska, Anita
• Is Part Of: Nonlinear analysis. Volume 39(2018)
• Page Start: 451
• Page End: 463
• Publication Date: 2018-02
• Subjects: Bifurcation -- Buckling -- Winkler foundation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.07.008
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our proof, based on the concept of the Brouwer degree, gives more, namely that from each bifurcation point there branches off a continuum of solutions.