On the existence and uniqueness of locally analytic invertible solutions of a system of nonlinear functional equations

  • Authors:

  • Nikolaos Kazantzis

  • Affiliations:

  • Department of Chemical Engineering, Worcester Polytechnic Institute, Worcester, MA

  • Venue:
  • Journal of Computational and Applied Mathematics
  • Year:
  • 2002

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Abstract

In the present research work, a set of necessary and sufficient conditions is derived, under which a rather broad class of nonlinear functional equations admits a unique locally analytic and invertible solution which can be easily computed with the aid of a symbolic software package. The main results naturally reproduce the solution of the linear problem, where the system of functional equations to be solved becomes equivalent to a Lyapunov matrix equation.