Oscillation Results for second-order quasi-linear neutral delay di erential equations

Abstract

In this paper, some new oscillation criteria are obtained for the second- order quasi-linear neutral delay differential equation r(t)| x(t) + p(t)x(τ (t)) |α−1 x(t) + p(t)x(τ (t)) + f t, x(σ(t)) = 0, t ≥ t0 under the case when ∞ t0 1 1 dt < ∞. Our results improve and supple- r α (t) ment some known results in the literature. An example is also provided to illustrate the main results.