# Monotone Schemes for Elliptic Systems, Periodic Solutions

## Abstract

In the previous chapters, the major method for proving the existence of steady state solutions for elliptic systems is Theorem 1.4-2 of the type of intermediate value theorem. It essentially uses maximum principle and the homo-topic invariance of degree. Another important technique for analyzing solutions of elliptic systems is the method of monotone schemes. Besides existence, it can be adapted to study uniqueness and stability for corresponding parabolic systems. Moreover, an analogous theory can be developed for finite difference systems. The corresponding monotone schemes provide numerical method for studying elliptic systems. The finite difference theory will be described in Chapter 6.

## Keywords

Periodic Solution Maximum Principle Elliptic System Parabolic System Lower Solution## Preview

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