The existence and uniqueness of solutions of a nonlinear toxin-dependent size-structured population model

Abstract

In this paper, we study a toxin-mediated size-structured population model with nonlinear reproduction, growth, and mortality rates. By using the characteristic method and the contraction mapping argument, we establish the existence-uniqueness of solutions to the model. We also prove the continuous dependence of solutions on initial conditions.

Keywords

• existence-uniqueness
• continuous dependence
• size-structured population
• characteristic method
• contraction mapping theorem