On the bifurcation of solutions to Marguerre–von Kármán equations

  • Tourkia Bendob

    Université Kasdi Merbah, Ouargla, Algeria
  • Abderrezak Ghezal

    Université Kasdi Merbah, Ouargla, Algeria
On the bifurcation of solutions to Marguerre–von Kármán equations cover

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Abstract

The objective of this work is to study the bifurcation of solutions of the Marguerre–von Kármán equations, which constitute a mathematical model for the buckling of Marguerre–von Kármán shallow shells. More precisely, we reduce the Marguerre–von Kármán equations to a single equation with a cubic operator; its second member depends on the function that defines the middle surface of the shallow shell and the applied forces. Next, we prove a general existence theorem for the reduced equation, by using the main theorem on pseudomonotone operators. Then we study the bifurcation of solutions in the reduced equation, with a second member, is small, at neighborhood of the simple characteristic value of the linearized problem.

Cite this article

Tourkia Bendob, Abderrezak Ghezal, On the bifurcation of solutions to Marguerre–von Kármán equations. Z. Anal. Anwend. 42 (2023), no. 3/4, pp. 331–358

DOI 10.4171/ZAA/1738