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Browsing by Subject "harmonic potential"

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    Item type:Article, Access status: Open Access ,
    Properties of the least action level and the existence of ground state solution to fractional elliptic equation with harmonic potential
    (Wydawnictwa AGH, 2024) Torres Ledesma, César E.; Gutierrez, Hernán C.; Rodríguez, Jesús A.; Bonilla, Manuel M.
    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