Reaction-diffusion equations or systems in bounded domains have been used to model many evolution processes in science and engineering, for example, Lotka-Volterra competitive and predator-prey systems, color pattern formation in butterflies and sea shells, tumor growth, just to mention a few in biology. Regardless of the details of the model, one of the common requirements is to investigate the spectral problem for an associated linear evolution problem. This is often required as a tool for nonlinear problems, for example when considering stability or invasion (in the ecological context).