Annual oscillation criteria for second-order nonlinear elliptic differential equations

In this paper, we present some new oscillation criteria for the second-order nonlinear elliptic differential equation ∇ · ( A ( x ) ∇ y ) + q ( x ) f ( y ) = e ( x ) , x ∈ Ω , where Ω is an exterior domain in R N . These criteria are different from most known ones in the sense that they are based on the information only on a sequence of annuals of Ω in R N , rather than on the whole exterior domain Ω . Also information about the distribution of the zero of solutions is obtained.