# Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation

Izydorek, Marek, Janczewska, Joanna, Waterstraat, Nils, Zgorzelska, Anita (2018) Bifurcation of equilibrium forms of an elastic rod on a two-parameter Winkler foundation. Nonlinear Analysis. Real World Applications, 39 . pp. 451-463. ISSN 1468-1218. (doi:10.1016/j.nonrwa.2017.07.008)

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http://dx.doi.org/10.1016/j.nonrwa.2017.07.008

## 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.

Item Type: Article 10.1016/j.nonrwa.2017.07.008 Bifurcation, Buckling, Winkler foundation Q Science > QA Mathematics (inc Computing science) > QA299 Analysis, CalculusQ Science > QA Mathematics (inc Computing science) > QA372 Ordinary differential equationsQ Science > QA Mathematics (inc Computing science) > QA801 Analytic mechanics Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Nils Waterstraat 05 Feb 2017 14:31 UTC 29 May 2019 18:38 UTC https://kar.kent.ac.uk/id/eprint/60224 (The current URI for this page, for reference purposes)