2017/01/20 by Alex H. Ardila, Alex Hernandez Ardila · 45 citations
Engineering · Mathematics · #Action (physics) #Advanced Mathematical Physics Problems #Applied mathematics #Cauchy problem #Compact space #Computer science #Initial value problem #Logarithm #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Nonlinear system #Physics #Quantum mechanics #Set (abstract data type) #Stability (learning theory) #Stability and Controllability of Differential Equations #math.AP #msc:35Q40 #msc:35Q55
paper · pdf · doi:10.1016/j.na.2017.01.006
published in Nonlinear Analysis 155, 52-64 (Elsevier BV) · 14 pages. Some minor typos have been corrected, to appear in Nonlinear Analysis T.M.A. arXiv admin note: text overlap with arXiv:1607.01479, arXiv:1611.03319, arXiv:1608.06929
arxiv created 2017/01/20 · openalex publication_date 2017/02/16 · arxiv updated 2017/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we consider the nonlinear fractional logarithmic Schrödinger equation. By using a compactness method, we construct a unique global solution of the associated Cauchy problem in a suitable functional framework. We also prove the existence of ground states as minimizers of the action on the Nehari manifold. Finally, we prove that the set of minimizers is a stable set for the initial value problem, that is, a solution whose initial data is near the set will remain near it for all time.