@inbook{f92d7a32e9404aa6aec865ed79eab1c4,

title = "On uniqueness for the generalized choquard equation",

abstract = "We consider the generalized Choquard equation describing trapped electron gas in three dimensional case. The study of orbital stability of the energy minimizers (known as ground states) depends essentially in the local uniqueness of these minimizers. The uniqueness of the minimizers for the case p = 2, i.e. for the case of Hartree–Choquard is well known. The main difficulty for the case p ≠ 2 is connected with possible lack of control on the Lp norm of the minimizers. Our main result treats the local uniqueness of radial positive minimizers for p ∈ (5∕3, 7∕3).",

keywords = "Choquard equation, Ground states, Local uniqueness",

author = "Vladimir Georgiev and George Venkov",

note = "Funding Information: Acknowledgments The first author was supported in part by INDAM, GNAMPA—Gruppo Nazionale per l{\textquoteright}Analisi Matematica, la Probabilit{\`a} e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, by Top Global University Project, Waseda University, the Project PRA 2018 49 of University of Pisa and project “Dinamica di equazioni nonlineari dispersive”, “Fondazione di Sardegna”, 2016. Funding Information: The first author was supported in part by INDAM, GNAMPA?Gruppo Nazionale per l?Analisi Matematica, la Probabilit? e le loro Applicazioni, by Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, by Top Global University Project, Waseda University, the Project PRA 2018 49 of University of Pisa and project ?Dinamica di equazioni nonlineari dispersive?, ?Fondazione di Sardegna?, 2016. The second author was supported in part by Research and Development Sector of the Technical University of Sofia. Funding Information: The second author was supported in part by Research and Development Sector of the Technical University of Sofia. Publisher Copyright: {\textcopyright} 2020, Springer Nature Switzerland AG.",

year = "2020",

doi = "10.1007/978-3-030-58215-9_11",

language = "English",

series = "Trends in Mathematics",

publisher = "Springer Science and Business Media Deutschland GmbH",

pages = "263--278",

booktitle = "Trends in Mathematics",

}