Electron. J. Diff. Eqns., Vol. 2008(2008), No. 153, pp. 1-13.

Critical Neumann problem for nonlinear elliptic systems in exterior domains

Shengbing Deng, Jianfu Yang

Abstract:
In this paper, we investigate the Neumann problem for a critical elliptic system in exterior domains. Assuming that the coefficient $Q(x)$ is a positive smooth function and $\lambda$, $\mu\geq0$ are parameters, we examine the common effect of the mean curvature of the boundary $\partial \Omega $ and the shape of the graph of the coefficient $Q(x)$ on the existence of the least energy solutions.

Submitted June 25, 2008. Published November 7, 2008.
Math Subject Classifications: 35J50, 35J60.
Key Words: Neumann problem; elliptic systems; exterior domains; critical Sobolev exponent; least energy solutions.

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  Shengbing Deng
Department of Mathematics, Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: shbdeng@yahoo.com.cn
Jianfu Yang
Department of Mathematics, Jiangxi Normal University
Nanchang, Jiangxi 330022, China
email: jfyang_2000@yahoo.com

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