Nonexistence of nonnegative solutions of elliptic systems of divergence type

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• 作者：Roberta Filippucci
• 关键词：Elliptic systems ; Nonexistence of entire weak solutions
• 刊名：Journal of Differential Equations
• 出版年：2011
• 出版时间：1 January 2011
• 年：2011
• 卷：250
• 期：1
• 页码：572-595
• 全文大小：258 K

文摘

In this paper we deal with noncoercive elliptic systems of divergence type, that include both the p-Laplacian and the mean curvature operator and whose right-hand sides depend also on a gradient factor. We prove that any nonnegative entire (weak) solution is necessarily constant. The main argument of our proofs is based on previous estimates, given in Filippucci (2009) [12] for elliptic inequalities. Actually, the main technique for proving the central estimate has been developed by Mitidieri and Pohozaev (2001) [23] and relies on the method of test functions. No use of comparison and maximum principles or assumptions on symmetry or behavior at infinity of the solutions are required.