Approximate solutions of generalized logistic equation

M. Onitsuka

This study investigates the behavior of the approximate solutions of the generalized logistic equation $y' = y\left(1-y^{\alpha}\right)$, where $\alpha>0$.
Based on the concept of Ulam stability, a concrete estimate of the amplitude of the difference between the approximate solution and the exact solution is obtained using the comparison principle and some sharp inequalities.
The obtained results can be applied to the nonautonomous Richards model $C'=r(t)C\left(1-\frac{C^{\alpha}}{K}\right)$.

Discrete and Continuous Dynamical Systems Series B

29

11

4505

4526

https://doi.org/10.3934/dcdsb.2024053