Monotone iterative technique for partial differential equations of first order

Abstract

In view of the fact that first-order partial differential equations arise naturally in modelling growth population of cells which constanctly change their properties, a study of stable and chaotic solutions of such equations was initiated in [3]. In this paper we develop monotone iterative technique for first-order partial differential equations and for this purpose we need to discuss existence, uniqueness and comparison results. We also indicate how the monotone sequences obtained may be employed as candidates for Lyapunov functions in stability theory.