@Article{TorresLedesma2024,
author = "Torres Ledesma, César E. and Gutierrez, Hernán C. and Rodríguez, Jesús A. and Bonilla, Manuel M.",
title = "Properties of the least action level and the existence of ground state solution to fractional elliptic equation with harmonic potential",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "5",
pages = "749--765",
doi = "https://doi.org/10.7494/OpMath.2024.44.5.749",
url = "https://doi.org/10.7494/OpMath.2024.44.5.749",
abstract = "In this article we consider the following fractional semilinear elliptic equation \[(-\Delta)^su+|x|^2u =\omega u+|u|^{2\sigma}u \quad \text{ in } \mathbb{R}^N,\] where \(s\in (0,1)\), \(N\gt 2s\), \(\sigma\in (0,\frac{2s}{N-2s})\) and \(\omega\in (0, \lambda_1)\). By using variational methods we show the existence of a symmetric decreasing ground state solution of this equation. Moreover, we study some continuity and differentiability properties of the ground state level. Finally, we consider a bifurcation type result.",
keywords = "harmonic potential, fractional Sobolev space, ground state solution, bifurcation result, variational method",
issn = "1232-9274"
}