Oscillation of Second-Order Sublinear Impulsive Differential Equations

Abstract

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-1x(τ(t))=0,t≠θk;Δx'(t)|t=θk+qk|x(τ(θk))|α-1x(τ(θk))=0;Δx(t)|t=θk=0,  (0<α<1)by considering the casesτ(t)≤tandτ(t)=t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.