A non-linear elastic plate model of moderate thickness: Existence, uniquenness and duality

Three problems are solved for a nonlinear model of elastic plates with transverse shear deformations. The material of the plate may be anisotropic. An existence theorem is formulated and proved for a class of boundary conditions. A uniqueness theorem is given for small loadings. The dual problem is derived and the minimax or Lagrangian approach is discussed.Dedicated to the memory of Paweek Telega, son of the second author