Ardila, Alex H.; Cely, Liliana; Squassina, Marco Logarithmic Bose-Einstein condensates with harmonic potential. (English) Zbl 1442.35413 Asymptotic Anal. 116, No. 1, 27-40 (2020). Summary: In this paper, by using a compactness method, we study the Cauchy problem of the logarithmic Schrödinger equation with harmonic potential. We then address the existence of ground states solutions as minimizers of the action on the Nehari manifold. Finally, we explicitly compute ground states (Gausson-type solution) and we show their orbital stability. Cited in 7 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35Q41 Time-dependent Schrödinger equations and Dirac equations 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general) 35A15 Variational methods applied to PDEs 35A01 Existence problems for PDEs: global existence, local existence, non-existence 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 35C08 Soliton solutions Keywords:logarithmic Schrödinger equation; harmonic potential; stability PDFBibTeX XMLCite \textit{A. H. Ardila} et al., Asymptotic Anal. 116, No. 1, 27--40 (2020; Zbl 1442.35413) Full Text: DOI arXiv