Integral manifolds for perturbed nonlinear differential equations

Abstract

We extend to perturbed nonlinear differential equations some of the basic integral manifold theorems of Bogoliubov-Mitropolski-Hale for perturbed linear systems. The technique involved uses a generalization of the variation of parameters formula. Implicit in the earlier work on perturbed linear systems is a uniqueness theorem for individual trajectories on half-lines which, to our knowledge, has never been proved. This theorem is critical in the arguments which were used to obtain the stability properties of the integral manifold and to establish its uniqueness. In the present paper an alternative development which avoids these arguments and retains the principal features of the theory is given.

This work was supported by the U.S. Army Research office, Durham,N.C.

This work was supported by the U.S. Army Research office, Durham,N.C.

Notes

This work was supported by the U.S. Army Research office, Durham,N.C.