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- Title
SUB-ELLIPTIC SYSTEMS INVOLVING CRITICAL HARDY-SOBOLEV EXPONENTS AND SIGN-CHANGING WEIGHT FUNCTIONS ON CARNOT GROUPS.
- Authors
JINGUO ZHANG
- Abstract
This article discusses the existence and multiplicity of positive solutions for subelliptic systems on Carnot groups. The authors use variational methods and the Nehari manifold to prove the existence of at least two positive solutions for certain parameter pairs. The article also explores the sub-Laplacian Hardy-Sobolev inequality and the difficulties in applying known techniques to the problem. The article presents several theorems proving the existence of positive solutions for different cases of nonlinearity. The article also provides preliminary results and definitions related to the Carnot group functional setting.
- Subjects
CARNOT cycle; MATHEMATICS; SOBOLEV spaces
- Publication
Journal of Nonlinear & Variational Analysis, 2024, Vol 8, Issue 2, p199
- ISSN
2560-6921
- Publication type
Article
- DOI
10.23952/jnva.8.2024.2.02