Abstract: In this paper, according to the simplified theory of [1], the bending of rectangular plates with two opposite edges simply supported and other two opposite edges being arbitrary under the action of a concentrated load is treated by means of properties of two-variable -function and the method of series [2], The effect of transverse shearing forces on the bending of plates is considered. When the thickness h of plates is small, and the term, whose orders are more than order of h² are neglected, then the results agree with the solutions corresponding to the problem of thin plates[3], At the end, the solutions of the bending problem of plates with arbitrary linear distributed load are also obtained.

Key words: nonlinear control system, integral along solution, dichotomy, global asymptotical behaviour, invariance principle