Positive solutions for a Kirchhoff problem of Brezis-Nirenberg type in dimension four

2024/05/27 by Giovanni Anello, Anello, Giovanni, Luca Vilasi +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2405.17055

openalex publication_date 2024/05/27 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28

Abstract

We consider a Kirchhoff problem of Brezis-Nirenberg type in a smooth bounded domain of ℝ⁴ with Dirichlet boundary conditions. Our approach, novel in this framework and based upon approximation arguments, allows us to cope with the interaction between the higher order Kirchhoff term and the critical nonlinearity, typical of the dimension four. We derive several existence results of positive solutions, complementing and improving earlier results in the literature. In particular, we provide explicit bounds of the parameters b and λ coupled, respectively, with the higher order Kirchhoff term and the subcritical nonlinearity, for which the existence of solutions occurs.

Related

• On the Brezis-Nirenberg problem for a Kirchhoff type equation in high dimension
• On Kirchhoff type equations with critical Sobolev exponent and Naimen's open problems
• Multiple positive solutions for a class of Kirchhoff type problems involving general critical growth
• Multiple positive solutions for Kirchhoff type problems involving concave and critical nonlinearities in R³
• The Brezis-Nirenberg problem in 4D