Generalized polynomial operators for nonlinear systems analysis

The concept of the so-called generalized polynomial operators is considered and applied especially to systems described by certain types of nonlinear differential equations. A theorem concerning local invertibility of polynomial operators is given. By an example it is shown how this theorem can be used to prove the existence of solutions, to construct those solutions, and to find a region of BIBO stability of the aforementioned systems. The treatment is quite general, being based on functional analysis. In particular, it can be applied to the systems analyzed by using functional series of Volterra type.