LIMIT-POINT/LIMIT-CIRCLE PROBLEM FOR SUB-HALF-LINEAR SECOND ORDER DELAY DIFFERENTIAL EQUATIONS

The authors investigate the limit-point and limit-circle properties of solutions of the delay differential equation a(t)|y ′ | p−1 y ′
′ + r(t)  y ϕ(t)
  λ sgn y ϕ(t)
= 0 where p ≥ λ ≥ 1, a(t) > 0, r(t) > 0, ϕ(t) ≤ t on R+, and limt→∞ ϕ(t) = ∞. The results generalize these properties for ordinary (non-delay) differential equations that were initiated by Hermann Weyl one hundred years ago for linear equations.