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.