Existence of positive equilibria for quasilinear models of structured population

TL;DR

This paper proves the existence of positive equilibrium solutions in quasilinear structured population models using Schauder's fixed point theorem, with applications to size-structured populations.

Contribution

It introduces a method to establish positive equilibria in quasilinear models, extending previous work to more general population structures.

Findings

Existence of positive stationary solutions is proven.

Application to size-structured population models demonstrates practical relevance.

Uses Schauder's fixed point theorem for the proof.

Abstract

In this paper I prove the existence of a positive stationary solution for a generic quasilinear model of structured population. The existence is proved using Schauder's fixed point theorem. The theorem is applied to a hierarchically size-structured population model.