Oscillation criteria for damped half-linear PDE via the integral operator

By using the integral operator, we establish some oscillation criteria for the damped half-linear PDE ∑ i , j = 1 N D i ( a i j ( x ) ‖ D y ‖ α − 1 D j y ) + 〈 b ( x ) , ‖ D y ‖ α − 1 D y 〉 + c ( x ) | y | α − 1 y = 0 . The results are extensions of integral averaging technique of Kamenev and include earlier results of Usami, Xu and Xing.