Necessary and Sufficient Oscillation Criteria for Discrete Reaction-Diffusion Equations

A number of oscillation criteria has been derived for discrete equations which models reaction-diffusion type processes (see e.g. [1,2]). These criteria provide sufficient conditions only, and therefore, necessary and sufficient conditions are desirable. In this note, we will show that the techniques of averaging and separation of variables can be used to obtain these criteria for a number of partial difference equations which models heat diffusions.