On the existence of solutions to the generalized Marguerre-von Kármán equations

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)83-100
Journal / PublicationMathematics and Mechanics of Solids
Issue number1
Publication statusPublished - Feb 2006


Using techniques from asymptotic analysis, the second author has recently identified equations that generalize the classical Marguerre-von Kármán equations for a nonlinearly elastic shallow shell by allowing more realistic boundary conditions, which may change their type along the lateral face of the shell. We first reduce these more general equations to a single "cubic" operator equation, whose sole unknown is the vertical displacement of the shell. This equation generalizes a cubic operator equation introduced by M. S. Berger and P. Fife for analyzing the von Kármán equations for a nonlinearly elastic plate. We then establish the existence of a solution to this operator equation by means of a compactness method due to J. L. Lions. © 2006 SAGE Publications.

Research Area(s)

  • Nonlinear partial differential equations, Nonlinear shallow shell theory