Berezansky, Leonid; Idels, Lev

Oscillation and asymptotic stability of a delay differential equation with Richard's nonlinearity

Electron. J. Differ. Equ. 2005, 21-27, electronic only (2005)


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

Mathematics Subject Classification

34K11, 34K20, 34K60


delay differential equations, richard's nonlinearity, oscillation, stability