A note on oscillation criteria for some perturbed half-linear elliptic equations

Abstract

In this paper, we show if the half-linear part of an equation is oscillatory, so would be some of its related perturbed equations. For one-dimentional cases, it can be resumed as the following: if the half-linear equation P(y) := {a(t)φ(y0)}0+c(t)φ(y) = 0 is oscillatory then any of its perturbed equations P(z)+Q0(t)h(y,y0) = 0 will also be oscillatory whenever Q ∈C1(R) and h ∈C(R2, R).