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We investigate bifurcation in the solution set of the von Kármán equations on a disk Ω ⊂ R 2 with two positive parameters α and β. The equations describe the behaviour of an elastic thin round plate lying on an elastic base under the action of a compressing force. The method of analysis is based on reducing the problem to an operator equation in real Banach spaces with a nonlinear Fredholm map F of index zero (to be defined later) that depends on the parameters α and β. Applying the implicitdoi:10.4064/ap77-1-5 fatcat:u5qrtw647revhkqswogfmjlkty