EXISTENCE OF LOWER AND UPPER SOLUTIONS IN REVERSE ORDER WITH RESPECT TO A VARIABLE IN A MODEL OF ACIDOGENESIS TO ANAEROBIC DIGESTION

Abstract

We prove existence of upper and lower solutions in reverse order with respect a part of the variables in a system of nonlinear ordinary dierential equations modelling acidogenesis in anaerobic digestion. The corresponding existence theorems are established. The upper and lower solutions are constructed analytically, by dening semi-trivial solutions for each of the variables in the model. We introduce the concept of indicator semi-trivial solutions. Finally, we numerically solve the system supported by the Matlab software and matching the graphs of the numerical solutions with analytical solutions is found.