IJPAM: Volume 69, No. 3 (2011)

ON THE OSCILLATION OF CERTAIN NONLINEAR
ELLIPTIC DIFFERENTIAL EQUATIONS

Gui-Bing Ou$^1$, Rong-Kun Zhuang$^2$
College of Science
Wuhan Textile University
Wuhan, 430073, P.R. CHINA
e-mail: gbouyang@sina.com
Department of Mathematics
Huizhou University
Huizhou, 516015, P.R. CHINA
e-mail: rkzhuang@163.com


Abstract. Using the integral average technique and a new function $H(r,s,l)$ defined in the sequel, some new oscillation criteria are obtained for second order elliptic differential equations with damping of the form

\begin{displaymath} \nabla\cdot(A(x)\nabla y)+B^T(x)\nabla y+q(x)f(y)=0,~~x\in\Omega,\end{displaymath}

where $\Omega $ is an exterior domain in $\mathbb{R}^N$. The main results are of a high degree of generality than many previous results.

Received: January 12, 2011

AMS Subject Classification: 35J60, 34C10

Key Words and Phrases: nonlinear elliptic differential equation, second order, generalized partial Riccati transformation, oscillation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 69
Issue: 3