Electron. J. Diff. Eqns., Vol. 2009(2009), No. 04, pp. 1-14.

Annulus oscillation criteria for second order nonlinear elliptic differential equations with damping

Rong-Kun Zhuang

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 2, 2009.
Math Subject Classifications: 35J60, 34C10.
Key Words: Nonlinear elliptic differential equation; second order; oscillation; annulus criteria.

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Rong-Kun Zhuang
Department of Mathematics, Huizhou University
Huizhou 516015, China
Department of Mathematics, Sun Yat-sen University
Guangzhou 510275, China
email: rkzhuang@163.com

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