Geodesic
Asymptotic properties of solutions of nonlinear Sharpe-Lotka model in the most general assumptions
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 227-240

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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.
Keywords: Sharpe-Lotka model, nonlinear integral equations, renewal equation. 
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     author = {A. N. Pichugina and B. Yu. Pichugin},
     title = {Asymptotic properties of solutions of nonlinear {Sharpe-Lotka} model in the most general assumptions},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {227--240},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a45/}
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A. N. Pichugina; B. Yu. Pichugin. Asymptotic properties of solutions of nonlinear Sharpe-Lotka model in the most general assumptions. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 227-240. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a45/