Abstract
In this paper we are interested on the existence of ground state solutions for fractional field equations of the form
where \({\alpha \in (0,1)}\) and f is an appropriate super-linear sub-critical nonlinearity. We prove regularity, exponential decay and symmetry properties for these solutions. We also prove the existence of infinitely many bound states and, through a non-local Pohozaev identity, we prove nonexistence results in the supercritical case.
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Felmer, P., Vergara, I. Scalar field equation with non-local diffusion. Nonlinear Differ. Equ. Appl. 22, 1411–1428 (2015). https://doi.org/10.1007/s00030-015-0328-z
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DOI: https://doi.org/10.1007/s00030-015-0328-z