Oscillatory and asymptotic behaviour of first order nonlinear differential equations with retarded argument \([t]\). (English) Zbl 0741.34046

The authors state without proofs a series of results concerned to the oscillatory and asymptotic behavior of the solutions of the delay differential equation \(x'(t)+p(t)f(x(t-[t]))=0\), \(t\geq 0\), where \(p\) is a continuous function on \([0,+\infty)\), \(p(t)\geq 0\) or \(p(t)\leq 0\), \(f(u)\) is a continuous function on \(\mathbb{R}\), \(f(0)=0\), \(uf(u)\geq 0\) for \(u\neq 0\).
Reviewer: M.Lizana (Caracas)


34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K20 Stability theory of functional-differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations