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On the fractional relativistic Schrödinger operator. (English) Zbl 1495.47074

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.

MSC:

47G30 Pseudodifferential operators
35R11 Fractional partial differential equations
42B35 Function spaces arising in harmonic analysis
35B09 Positive solutions to PDEs
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