Periodically forced nonlinear systems of difference equations

The existance of nontrivial (x=0( periodic solutions of a general class of periodic nonlinear difference equations is proved using bifurcation theory methods. Specifically, the existance of a global continuum of nontrivial periodicsolutions that bifurcates from the trivial solution (x=0) is proved. Conditions are given under which the nontrivial solutions are positive. A prerrequisite Fredholm and adjoint operator theory for linear periodic systems is developed. An application to application dynamics is made.