The solvability of Brezis-Nirenberg type problems of singular quasilinear elliptic equation

2004/03/31 by Benjin Xuan, Xuan, Benjin
Computer Science · Mathematics · #35J60 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #math.AP #msc:35J60

paper · pdf · doi:10.48550/arxiv.math/0403549

24 pages, no figure

arxiv created 2004/03/31 · openalex publication_date 2004/03/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the existence and non-existence of non-trivial solution to a Brezis-Nirenberg type problem with singular weights. First, we obtain a compact imbedding theorem which is an extension of the classical Rellich-Kondrachov compact imbedding theorem, and consider the corresponding eigenvalue problem. Secondly, we deduce a Pohozaev type identity and obtained a non-existence result. Thirdly, based on a generalized concentration compactness principle, we will give some abstract conditions when the functional satisfies the (PS)_c condition. Finally, based on the explicit form of the extremal function, we will obtain some existence results to the problem.

Citations

• A relation between pointwise convergence of functions and convergence of functionals

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