ABSTRACT
One of the widely used comparison methods for reaction diffusion systems is the method of upper and lower solutions. This method gives not only existence-comparison theorems for both parabolic and elliptic equations, suitable construction of upper and lower solutions can lead to various qualitative property of the system, including multiplicity of steady-state solutions, stability and instability of steady-state solutions, and blowing-up behavior of time-dependent solutions (cf. [1, 3-5, 7, 10, 11, 14]). It can also be used to develop computational algorithms for numerical solutions of the corresponding discrete reaction diffusion equations (e.g. see [6, 12, 13]). In this presentation we give an overview of the method for a class of finite coupled reaction diffusion systems and its application to the stability analysis and traveling wave solutions of some model problems arising from ecology.
