Abstract

We derive new sufficient conditions for global attractivity in nonlinear delay differential equations using a mixed monotone technique. The equations considered include the equation of the form d/dt[x(t) − ax(t − τ)] = − μx(t) − bx(t − σ) + f(x(t − γ)), where a, b, μ, −, σ, and γ are nonnegative numbers such that a ε [0, 1), b + μ > 0 and λ(1 − ae^−λτ) = − μ − be^{− λσ} has a negative root; moreover f(x) is a mixed monotone function, that is, f(x) = ω(x, x), where ω(x, y) is monotone decreasing in x and increasing in y. Our results are applied to some delay differential equations from mathematical biology.

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^* On leave from Computing Centre, A. Szent-Györgyi Medical University, H-6720 Szeged, Hungary, Pécsi ut 4/a.