On the existence of Nehari ground states for the nonlinear Schrödinger equation on discrete graphs
Analysis and Mathematical Physics, vol.16, no.4, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 16 Issue: 4
- Publication Date: 2026
- Doi Number: 10.1007/s13324-026-01237-z
- Journal Name: Analysis and Mathematical Physics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: Discrete graph, Generalized Nehari manifold, Nonlinear Schrödinger equation
- Open Archive Collection: AVESIS Open Access Collection
- Dokuz Eylül University Affiliated: Yes
Abstract
We study standing waves for the nonlinear Schrödinger equation on a discrete graph. We characterize for a self-adjoint realizations of Schrödinger operators conditions related with the geometry of the graph that guarantee discreteness of the spectrum and study ground states on the generalized Nehari manifold in order to prove the existence of standing wave solutions in the self-focusing and defocusing cases. In this context, we show properties of the solutions, such as integrability. Finally, we discuss decay properties of solutions and the bifurcation of solutions from the trivial solution.