Affiliations: [a] Instituto Nacional de Matemática Pura e Aplicada – IMPA, Estrada Dona Castorina, 110 CEP 22460-320, Rio de Janeiro, RJ, Brasil. E-mail: [email protected] | [b] Instituto de Matemática e Estatística, Departamento de Matemática, Universidade de São Paulo, 05508-090, São Paulo, SP, Brazil. E-mail: [email protected] | [c] Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia, Italy. E-mail: [email protected]
Note: [**] Member of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA).
Abstract: 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.
