The nonlinear neutral differential equation dn/dt n[x(t)+h(t)x(τ(t))]+f(t,x(g(t)))=q(t), is considered under the following conditions: n∈N; h∈C[t0,∞); τ∈C[t0,∞) is strictly increasing, limt→∞τ(t)=∞ and τ(t)<t for t>t0; g∈C[t0,∞) and lim t→∞g(t)=∞; f∈C([t0,∞)×R) ; q∈C[t0,∞). It is shown that if f is small enough in some sense, Eq. (1) has a solution x(t) which behaves like the solution of the unperturbed equation dn/dtn[ω(t)+h(t) ω(τ(t))]=q(t). Several known results in the literature can be obtained from our results.
- Neutral differential equation
- Nonoscillatory solution
- Oscillatory solution
ASJC Scopus subject areas
- Modelling and Simulation
- Computer Science Applications