Convergence and ultimate bounds of solutions of the nonautonomous Volterra-Lotka competition equations.(English)Zbl 0648.34037

The author considers the nonautonomous system of differential equations $u'(t)=u(t)(a(t)-b(t)u(t)-c(t)v(t))$
$v'(t)=v(t)(d(t)-e(t)u(t)- f(t)v(t))$ where the functions a,...,f are assumed to be continuous and bounded above and below by positive constants on some half-infinite interval $$t_ 0\leq t<+\infty$$. He shows that there is a solution $$col(u_ 0(t),v_ 0(t))$$ for which the inequalities $$0<s_ 1\leq u_ 0(t)\leq r_ 1$$, $$0<r_ 2\leq v_ 0(t)\leq s_ 2$$ hold for $$t_ 0\leq t<+\infty$$. If there are two solutions of that kind then their difference tends to zero as $$t\to +\infty$$.
Reviewer: L.Reizins

MSC:

 34C11 Growth and boundedness of solutions to ordinary differential equations
Full Text:

References:

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