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


34C11 Growth and boundedness of solutions to ordinary differential equations
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