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 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. © 2011 A. Zafer.