Description of the solution set of the von Kármán equations for a circular plate in a small neighbourhood of a simple bifurcation point

Abstract

In this work we study the von Kármán system for a thin circular elastic plate fixed to the elastic base and subjected to the compressing force along its boundary. The system is composed of two fourth-order nonlinear partial differential equations that give a valid mathematical description of the buckling of the plate. We intend to demonstrate the applicability of nonlinear functional analysis in the study of this problem. We describe the solution set of the von Kármán equations in a small neighbourhood of a simple bifurcation point.2000 Mathematics Subject Classification: 35Q72, 46T99.