On the existence of Nehari ground states for the nonlinear Schrödinger equation on discrete graphs
Analysis and Mathematical Physics, cilt.16, sa.4, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16 Sayı: 4
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s13324-026-01237-z
- Dergi Adı: Analysis and Mathematical Physics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Discrete graph, Generalized Nehari manifold, Nonlinear Schrödinger equation
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Dokuz Eylül Üniversitesi Adresli: Evet
Özet
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.