Asymptotic properties of solutions of nonlinear Sharpe-Lotka model in the most general assumptions

In the papers [6, 7, 8] based on Sharpe-Lotka model [1, 2] was constructed and studied nonlinear integral model of dynamics of isolated populations with the self-limitation and the finite lifetime of individuals. In 2002 has been proved that the solution of this model has the limit in the case when the equation $\lambda(x) = \beta$ has no more than one root. In this paper we prove that the limit of the solution of the model exists independently of the number of roots of the equation $\lambda(x) = \beta$. In addition, using the results of [9], greatly weakened conditions on model parameters. Furthermore, the theorem on the continuous dependence on the initial data and the stability theorem was proved.