An existence theorem for generalized von Kármán equations (Q2738880)

Using techniques from formal asymptotic analysis [\textit{P. G. Ciarlet} and \textit{L. Gratie}, ibid. 331, 329--335 (2000; Zbl 0963.35037) and J. Math. Pures Appl., IX. Sér. 80, 263--279 (2001; Zbl 1055.35051)], the first two authors have identified ``generalized von Kármán equations'', which constitute a two-dimensional model for a special nonlinearly elastic plate. For it only a portion of the lateral face is subjected to boundary conditions of von Kármán's type, the remaining portion is free. In the paper an existence theorem for these equations is established as a compactness method due to \textit{J.-L. Lions} [Quelques méthodes de résolution des problèmes aux limites non linéaires (Études mathématiques, Dunod, Paris) (1969; Zbl 0189.40603)] is adapted.