Schrödinger systems with critical coupling in $$ \mathbb {R}^N$$
Abstract
Abstract This paper is concerned with the existence and multiplicity of positive solutions for nonlinear Schrödinger systems in $$ \mathbb {R}^N$$ R N with a critical weak coupling. The existence of a positive least energy solution is also studied. The proofs of the main results rely on local and global minimization arguments and minimax methods applied to an associated functional restricted to the Nehari manifold. Appropriated estimates for the critical levels, based on the argument of Brezis and Nirenberg for the scalar problem, are a key ingredient to deal with the lack of compactness of the functional.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Advanced Mathematical Physics Problems
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Calculus of Variations and Partial Differential Equations
- Volume
- 65
- Issue
- 3
- Publication date
- 17 February 2026
- Language
- EN