A Gompertz model with conditional Hyers-Ulam stability

D. R. Anderson, M. Kondo, and M. Onitsuka

We consider the Hyers-Ulam stability of a first-order nonlinear differential equation based on the Gompertz model. The stability is conditionally established, based on the maximum size of the perturbation being sufficiently small and the initial condition being sufficiently large. The Hyers-Ulam stability constant is derived directly using the comparison principle and sharp inequalities. Illustrative examples and numerical experiments are presented to demonstrate the findings. Finally, future directions for this study are also presented.

Mathematical Methods in the Applied Sciences

https://doi.org/10.1002/mma.11150