An integral oscillation criterion for even order half-linear differential equations

Abstract

Integral tests for detection of oscillatory behavior of solutions of even order half-linear differential equations of the form Lnx+q(t)|x|βsgnx=0,t≥a>0,(A)where L1x(t)=x′(t),Li+1x(t)=[pi(t)|Lix(t)|αisgnLix(t)]′,i=1,…n−1,αi,1≤i≤n−1, and β being positive constants and pi,1≤i≤n−1, and q continuous functions from [a,∞) to (0,∞), are established in the case where α1⋯αn−1=β.