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Coexistence solutions of the unstirred chemostat model with internal storage. (Chinese. English summary) Zbl 1449.35270

Summary: The existence of positive steady state solutions of an unstirred chemostat model with internal storage is studied. Due to the singularity arising from the ratio terms in this model, standard technique such as linearization and bifurcation can not be applied here. In order to overcome the mathematical difficulties caused by the singularity in the ratio terms, the sharp priori estimates for positive steady state solutions of the system are established firstly, which ensure that all positive steady state solutions of the system belong to a special cone. Secondly, some sufficient conditions for the existence of positive steady state solutions are given by using the principle eigenvalues of associated nonlinear eigenvalue problems and the degree theory in the special cone.

MSC:

35K57 Reaction-diffusion equations
35B09 Positive solutions to PDEs
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