Kiguradze-type Oscillation Theorems for Second Order Superlinear Dynamic Equations on Time Scales

Abstract

AbstractConsider the second order superlinear dynamic equationwherep∈C(, ℝ),is a time scale,ƒ: ℝ → ℝ is continuously differentiable and satisfiesƒ′(x) > 0, andx ƒ(x) > 0 forx≠ 0. Furthermore,f(x) also satisfies a superlinear condition, which includes the nonlinear functionƒ(x) =xαwith α > 1, commonly known as the Emden–Fowler case. Here the coefficient functionp(t) is allowed to be negative for arbitrarily large values oft. In addition to extending the result of Kiguradze for (∗) in the real case= ℝ, we obtain analogues in the difference equation andq-difference equation cases.