On the Brezis-Nirenberg problem for a Kirchhoff type equation in high dimension

F. Faraci; K. Silva

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arXiv · 2006.05934

On the Brezis-Nirenberg problem for a Kirchhoff type equation in high dimension

F. Faraci·K. Silva

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Abstract

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.

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F. Faraci, K. Silva. 2020-06-10. On the Brezis-Nirenberg problem for a Kirchhoff type equation in high dimension. https://arxiv.org/abs/2006.05934

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