Oscillation and Nonoscillation Theorems for a Class of Fourth Order Quasilinear Generalized α-Difference Equations

In this paper, we consider certain generalized quasilinear α − difference equations ( ) 2 2 2 1 1 ( ) ( ) ( ) | ( )| ( ) ( )| ( ( ))| ( ( )) = 0 v k v k q k v k v k γ β ∆ ∆ ∆ + α α α − σ σ − l l l Where γ β, are positive constants; q k( ) are positive real valued function, k0 0 ∈K = {1, 2, } L . An oscillation and nonoscillation theorem of the above equation is obtained.