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Oscillation and asymptotic stability of a delay differential equation with Richard’s nonlinearity. (English) Zbl 1085.34051

Summary: We obtain sufficient conditions for oscillation of solutions and for asymptotical stability of the positive equilibrium of the scalar nonlinear delay differential equation \[ \frac{dN}{dt} = r(t)N(t)\Big[a-\Big(\sum_{k=1}^m b_k N(g_k(t)) \Big)^{\gamma}\Big] \] with \(g_k(t)\leq t\) .

MSC:

34K11 Oscillation theory of functional-differential equations
34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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