Annulus Criteria for Oscillation of Second Order Damped Elliptic Equations

Some annulus oscillation criteria are established for the second order damped elliptic differential equation N X i,j=1 Di[aij(x)Djy] + N X i=1 bi(x)Diy + C(x, y) = 0 under quite general assumption that they are based on the information only on a sequence of annuluses of Ω(r0) rather than on the whole exterior domain Ω(r0). Our results are extensions of those due to Kong for ordinary differential equations. In particular, the results obtained here can be applied to the extreme case such as R Ω(r0) c(x)dx = −∞.