On the fractional relativistic Schrödinger operator
This paper concerns the fractional relativistic Schrödinger equation defined by \((-\Delta+m^2)^su=g(x,u)\in \mathbb{R}^N\). Several works have recently shown some interesting results regarding existence and multiplicity of solutions for the equation. In this paper, the author analyzes specific behaviors of the solutions such as regularity, decay, and symmetry. To be specific, the results include \(L^\infty\)- regularity, exponential decay, a~Pohozaev-type identity, and the radial symmetry of the solutions. The results in this paper are established by exploiting fractional Sobolev spaces and properties of Bessel functions.
scientific article; zbMATH DE number 7436215
scientific article