The Dynamics Of The Solution Semigroups Of First Order Quasi-linear Lasota Equations

This article concerns the asymptotic behaviour of the dynamical systems induced by the Lasota equation.We study chaoticity of the system in the sense of Devaney and the topological transitivity and strong stability of non-autonomous systems in different phase spaces.There are two main aspects:On the one hand,we study the chaoticity of Lasota equation:(?)in the sense of Devaney in the space V={v∈Lp:v(0)=0} by constructing the right inverse operator;On the other hand,we discuss the topological transitivity and strong stability of Lasota equations:(?)and(?)in different phase spaces(Lp,(?)p,Vα,Lφ).We generalize and improve some results of the existing literature.