Existence and non-existence results for cooperative elliptic systems without variational structure

John Villavert
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引用次数: 0

Abstract

We consider general cooperative elliptic systems possibly without variational structure and with differential operator resembling that from an Euler–Lagrange equation for a sharp Hardy–Sobolev inequality. Under suitable growth conditions on the source nonlinearities and geometric assumptions on the domain, we derive various existence and non-existence results and Liouville theorems. The results are obtained by incorporating and adapting various techniques, including variants of the method of moving planes enhanced by Kelvin and Emden–Fowler type transformations, as well as degree theoretic shooting methods.

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无变结构合作椭圆系统的存在与不存在结果
我们考虑的一般合作椭圆系统可能没有变分结构,其微分算子类似于尖锐 Hardy-Sobolev 不等式的欧拉-拉格朗日方程。在适当的源非线性增长条件和域几何假设下,我们推导出各种存在和不存在结果以及Liouville定理。这些结果是通过结合和调整各种技术得出的,包括通过开尔文和埃姆登-福勒类型变换增强的移动平面方法的变体,以及度论射影方法。
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