In this work we consider the existence of positive singular solutions

$ \begin{equation} \left\{ \begin{array}{lcl} \hfill -\Delta u_1 & = & \lambda_1 | \nabla u_2|^p \qquad \mbox{ in } \Omega, \\ \hfill -\Delta u_2 & = & \lambda_2 | \nabla u_1|^q \qquad \mbox{ in } \Omega, \\ \hfill u_1 = u_2 & = & 0 \hfill \mbox{ on } \partial \Omega, \end{array}\right. \end{equation} $

中文翻译：

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Lane-Emden系统的奇异解

在这项工作中，我们考虑了正奇异解的存在

$ \ begin {equation} \ left \ {\ begin {array} {lcl} \ hfill-\ Delta u_1＆=＆\ lambda_1 | \ nabla u_2 | ^ p \ qquad \ mbox {in} \ Omega，\\ \ hfill-\ Delta u_2＆=＆\ lambda_2 | \ nabla u_1 | ^ q \ qquad \ mbox {in} \ Omega，\\ \ hfill u_1 = u_2＆=＆0 \ hfill \ mbox {on} \ partial \ Omega，\ end {array} \ right。\ end {equation} $