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Oscillation of second-order sublinear impulsive differential equations. (English) Zbl 1223.34049

Summary: Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type:

x '' (t)+p(t)|x(τ(t))| α-1 x(τ(t))=0,tθ k ;
Δx ' (t)| t=θ k +q k |x(τ(θ k ))| α-1 x(τ(θ k ))=0;Δx(t)| t=θ k =0,(0<α<1)

by considering the cases τ(t)t and τ(t)=t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.

MSC:
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A37Differential equations with impulses