Janczewska, Joanna Description of the solution set of the von Kármán equations for a circular plate in a small neighbourhood of a simple bifurcation point. (English) Zbl 1387.35186 NoDEA, Nonlinear Differ. Equ. Appl. 13, No. 3, 337-348 (2006). Summary: 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. MSC: 35J56 Boundary value problems for first-order elliptic systems 35B32 Bifurcations in context of PDEs 35J40 Boundary value problems for higher-order elliptic equations 35Q74 PDEs in connection with mechanics of deformable solids 47J15 Abstract bifurcation theory involving nonlinear operators 74G60 Bifurcation and buckling 74K20 Plates PDF BibTeX XML Cite \textit{J. Janczewska}, NoDEA, Nonlinear Differ. Equ. Appl. 13, No. 3, 337--348 (2006; Zbl 1387.35186) Full Text: DOI