We establish a general result for estimating the upper average of a continuous and bounded function over an infinite interval. As an application, we show that a previously studied model of microbial growth in a chemostat with time–varying nutrient input admits solutions (populations) that exhibit weak persistence but not weak average persistence.
Journal of Inequalities in Pure and Applied Mathematics
Ellermeyer, S. (2009). On the estimation of averages over infinite intervals with an application to average persistence in population models. Journal of Inequalities in Pure and Applied Mathematics, 10(4), Art. 93, 8pp.