# American Institute of Mathematical Sciences

November  2002, 2(4): 541-560. doi: 10.3934/dcdsb.2002.2.541

## Global stability for differential equations with homogeneous nonlinearity and application to population dynamics

 1 Unité de Biométrie, INRA, 78352 Jouy-en-Josas, Cedex, France

Received  October 2001 Revised  May 2002 Published  August 2002

In this paper we investigate global stability for a differential equation containing a positively homogeneous nonlinearity. We first consider perturbations of the infinitesimal generator of a strongly continuous semigroup which has a simple dominant eigenvalue. We prove that for "small" perturbation by a positively homogeneous nonlinearity the qualitative properties of the linear semigroup persist. From this result, we deduce a global stability result when one adds a certain type of saturation term. We conclude the paper by an application to a phenotype structured population dynamic model.
Citation: Pierre Magal. Global stability for differential equations with homogeneous nonlinearity and application to population dynamics. Discrete & Continuous Dynamical Systems - B, 2002, 2 (4) : 541-560. doi: 10.3934/dcdsb.2002.2.541
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