A remark on the radial and nonradial solutions for an elliptic system with a quadratic gradient term

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• 作者：Bogdan Constantin ^{tica1234ticabogd@yahoo.com}
• 关键词：Entire solution ; Large solution ; Elliptic system
• 刊名：Applied Mathematics and Computation
• 出版年：2013
• 出版时间：1 April, 2013
• 年：2013
• 卷：219
• 期：15
• 页码：8302-8310
• 全文大小：245 K

文摘

Recently, the authors Yang and Zhang in [Y. Yang, X. Zhang, Entire blow-up solutions of semilinear elliptic system with quadratic gradient term, Abstract and Applied Analysis, 2012] have been obtained sufficiently conditions for the existence and non-existence of radially symmetric solutions for the system of equations on () with and . Our aim in this paper is to give a necessary and a sufficient condition, but for the existence of large (or explosive) solutions for the same class of systems. Moreover, we intend to obtain a non-radial solution for the considered problem. We also point out that our framework in the obtained results improve and complete some of the results obtained by Yang and Zhang.