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

被引：28

作者：

Faraci, F. ^{[1
]}

Silva, K. ^{[2
]}

机构：

[1] Univ Catania, Dept Math & Comp Sci, I-95125 Catania, Italy

[2] Univ Fed Goias, Inst Matemat & Estat, BR-74001970 Goiania, Go, Brazil

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 60卷 / 01期

关键词：

35J20; 35B33;

D O I：

10.1007/s00526-020-01891-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：33

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