Journal of the
Korean Mathematical Society JKMS

Some annulus oscillation criteria are established for the second order damped elliptic differential equation \begin{equation*} \sum_{i,j=1}^N D_i[a_{ij}(x)D_j y] + \sum _{i=1}^Nb_i(x)D_iy+C(x,y)=0 \end{equation*} under quite general assumption that they are based on the information only on a sequence of annuluses of $\Omega(r_0)$ rather than on the whole exterior domain $\Omega(r_0)$. 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 $\int_{\Omega(r_0)}c(x)dx=-\infty$.

Keywords: oscillation, annulus criteria, elliptic equations, second order, damped

MSC numbers: 35B05, 35J15, 35J60