Abstract The paper deals with the existence of solutions for ( p , Q ) (p,Q) coupled elliptic systems in the Heisenberg group, with critical exponential growth at infinity and singular behavior at the origin. We derive existence of nonnegative solutions with both components nontrivial and different, that is solving an actual system, which does not reduce into an equation. The main features and novelties of the paper are the presence of a general coupled critical exponential term of the Trudinger-Moser type and the fact that the system is set in ℍ n {{\mathbb{H}}}^{n} .

中文翻译：

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(p,Q) 海森堡群中具有临界奇异指数非线性的系统

摘要 本文讨论了海森堡群中 ( p , Q ) (p, Q) 耦合椭圆系统的解的存在性，在无穷远处具有临界指数增长，在原点处具有奇异行为。我们推导出具有非平凡和不同分量的非负解的存在，即求解一个实际系统，它不会简化为方程。该论文的主要特点和新颖之处在于存在 Trudinger-Moser 类型的一般耦合临界指数项以及系统设置在 ℍ n {{\mathbb{H}}}^{n} 中的事实。