Unilateral eigenvalue problems for nonlinearly elastic plates and pseudo-monotone operators

Abstract

We consider a class of variational inequalities that model the buckling of a nonlinearly elastic thin plate, clamped on a part of its boundary and lying on a flat rigid support. The existence and bifurcation results of D. Goeleven, V.H. Nguyen and M. Thera rely on the Leray-Schauder degree. In this Note, using the topological degree for pseudomonotone operators of type (S +), we establish a more general existence result for such variational inequalities of von Karman type.