On a fractional harmonic oscillator: existence and inexistence of solution, regularity and decay properties

Hamilton P. Bueno, Aldo H. S. Medeiros, Olimpio H. Miyagaki +1

Under simple hypotheses on the nonlinearity $f$, we consider the fractional harmonic operator problem \begin{equation}\label{abstr}\sqrt{-Δ+|x|^2}\,u=f(x,u)\ \ \textrm{in }\ \mathb…