TY  - JOUR
ID  - TorresLedesma2024
LB  - TorresLedesma2024
AU  - Torres Ledesma, César E.
AU  - Gutierrez, Hernán C.
AU  - Rodríguez, Jesús A.
AU  - Bonilla, Manuel M.
TI  - Properties of the least action level and the existence of ground state solution to fractional elliptic equation with harmonic potential
ST  - Properties of the least action level and the existence of ground state solution to fractional elliptic equation with harmonic potential
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 5
SP  - 749
EP  - 765
DO  - https://doi.org/10.7494/OpMath.2024.44.5.749
UR  - https://doi.org/10.7494/OpMath.2024.44.5.749
AB  - 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.
KW  - harmonic potential
KW  - fractional Sobolev space
KW  - ground state solution
KW  - bifurcation result
KW  - variational method
SN  - 1232-9274
ER  -