Existence results for a superlinear singular equation of Caffarelli-Kohn-Nirenberg type

2004/04/02 by Benjin Xuan, Xuan, Benjin
Mathematics · #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35J60

paper · pdf · doi:10.48550/arxiv.math/0404035

13 pages, no figure

arxiv created 2004/04/02 · arxiv updated 2009/12/01

Abstract

In this paper, using Mountain Pass Lemma and Linking Argument, we prove the existence of nontrivial weak solutions for the Dirichlet problem for the superlinear equation of Caffarelli-Kohn-Nirenberg type in the case where the parameter λ∈ (0, λ₂), λ₂ is the second positive eigenvalue of the quasilinear elliptic equation of Caffarelli-Kohn-Nirenberg type.

Related

• Regularity of solutions for a class of quasilinear elliptic equations related to Caffarelli-Kohn-Nirenberg inequality
• A note on regularity of solutions to degenerate elliptic equations of Caffarelli-Kohn-Nirenberg type
• A variational problem associated to a hyperbolic Caffarelli--Kohn--Nirenberg inequality
• Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems
• The solvability of Brezis-Nirenberg type problems of singular quasilinear elliptic equation