In this paper we extend some results from our earlier work [ 11, where additional
The buckling of a thin clamped plate can be described by a function u (xl, x2) information about the model and its operator equation can be found. defined in a bounded domain Q ' 3 2 , being a solution of the equation
with operators B E (I@: X p 2 --t I@:), DO E (m: --t I@;) and the constant y =-0, depending on physical and geometrical properties of the plate. The HILBERT space W i is the closure of the manifold in the SOBOLEV space W&Q) ; its elements are subdued to the geometrical boundary conditions of a clamped plate. In osder to secure the validity of GAUSS formula and some inbedding theorems, we accept the necessary regularity conditions on a 0 which in fact cause no loss of generality with respect to possible shapes of real plates. The space C,(D) consits of all real functions which are continuous together with their partial derivatives up to order four in the closure a = Q U aQ. Below we consider the space WE as closure of C4(D) with the norm ~scalar product (u, v) and norm llull= l(u, 20) in mi are defined by In order t o define the operator B we start from the expression