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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
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
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