论文标题
关于Kirchhoff类型方程的Brezis-Nirenberg问题高维
On the Brezis-Nirenberg problem for a Kirchhoff type equation in high dimension
论文作者
论文摘要
本文处理的是参数化的基尔乔夫类型问题，涉及高维度的关键非线性。在亚临界扰动的效果下，通过将变异性质与仔细分析与问题相关的能量功能的纤维图相结合，从而在亚临界扰动的效果下获得了溶液的存在。还解决了纯电扰动的特殊情况。通过对Nehari歧管的研究，我们将一般情况扩展到更广泛的参数范围。
The present paper deals with a parametrized Kirchhoff type problem involving a critical nonlinearity in high dimension. Existence, non existence and multiplicity of solutions are obtained under the effect of a subcritical perturbation by combining variational properties with a careful analysis of the fiber maps of the energy functional associated to the problem. The particular case of a pure power perturbation is also addressed. Through the study of the Nehari manifolds we extend the general case to a wider range of the parameters.
