Oscillation Criteria for Second-Order Superlinear Neutral Differential Equations

Abstract EN

Some oscillation criteria are established for the second-order superlinear neutral differential equations (r(t)|z'(t)|α-1z'(t))'+f(t,x(σ(t)))=0, t≥t0, where z(t)=x(t)+p(t)x(τ(t)), τ(t)≥t, σ(t)≥t, p∈C([t0,∞),[0,p0]), and α≥1.

Our results are based on the cases ∫t0∞1/r1/α(t)dt=∞ or ∫t0∞1/r1/α(t)dt<∞.

Two examples are also provided to illustrate these results.