Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 04, pp. 1-14.

Title: Annulus oscillation criteria for  second order
       nonlinear elliptic  differential equations with damping
   
Author: Rong-Kun Zhuang (Huizhou Univ., Huizhou, China)

Abstract:
 We establish oscillation criteria for the second-order
 elliptic differential equation
 $$
 \nabla\cdot(A(x)\nabla y)+B^T(x)\nabla y+q(x)f(y)=e(x), \quad
 x\in\Omega,
 $$
 where $\Omega $ is an exterior domain in $\mathbb{R}^N$.  These
 criteria are different from most known ones in the sense that they
 are based on the information only on  a sequence  of annulus
 of $\Omega$, rather than on the whole exterior domain $\Omega$.
 Both the cases when $\frac{\partial b_i}{\partial x_i}$ exists
 for all $i$  and when it does not exist for some $i$ are considered.
 
Submitted May 28, 2008. Published January 02, 2009.
Math Subject Classifications: 35J60, 34C10.
Key Words: Nonlinear elliptic differential equation; second order;
           oscillation; annulus criteria.