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Oscillation criteria for second-order delay dynamic equations on time scales. (English) Zbl 1147.39002

The paper deals with the following second order nonlinear delay dynamic equation on a time scale

(p(t)(x (t)) γ ) +q(t)f(x(τ(t)))=0,tT

where T is a time scale. For oscillation analysis, two cases are considered

a) a 1 p(t) 1/γ Δt=,b) a 1 p(t) 1/γ Δt<·

The main criterion of oscillation follows from the divergence of the integral

lim sup t a t Lk γ q(s)δ(s)τ(s) σ(s) γ -p(s)(δ (s)) + γ+1 (γ+1) γ+1 (δ(s)) γ Δs=

for some pC rd 1 ([a,),), p>0, k(0,1) and some δ(s)>0, δ + =max{0,δ}.

39A11Stability of difference equations (MSC2000)
39A12Discrete version of topics in analysis
[1] · doi:10.1007/BF03323153
[5] · Zbl 1075.34028 · doi:10.1216/rmjm/1181069797
[7] · Zbl 1050.34042 · doi:10.1112/S0024610703004228
[22] · Zbl 0272.34095 · doi:10.4153/CMB-1973-011-1