An Ambrosetti-Prodi type exact multiplicity result is proved for a diffusive logistic equation with harvesting. We show that a modified diffusive logistic mapping has exactly either zero, or one, or two pre-images depending on the harvesting rate. It implies that the original diffusive logistic equation with harvesting has at most two positive steady state solutions.
['Yanan Wang', 'Yuwen Wang', 'Junping Shi']
Exact multiplicity of solutions to a diffusive logistic equation with harvesting