caa a22 4500 606194304 CHVBK 20210128100913.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00030-015-0328-z doi (NATIONALLICENCE)springer-10.1007/s00030-015-0328-z Scalar field equation with non-local diffusion [Elektronische Daten] [Patricio Felmer, Ignacio Vergara] In this paper we are interested on the existence of ground state solutions for fractional field equations of the form $$\left\{\begin{array}{ll} (I - \Delta)^{\alpha}u = f(x, u) & \quad {\rm in} \, I\!R^N,\\ u > 0 & \quad {\rm in} \, I\!R^N, \quad \displaystyle\lim_{|x| \to \infty}u(x) = 0,\end{array}\right.$$ ( I - Δ ) α u = f ( x , u ) in I R N , u > 0 in I R N , lim | x | → ∞ u ( x ) = 0 , where $${\alpha \in (0,1)}$$ α ∈ ( 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. Springer Basel, 2015 Felmer Patricio Departamento de Ingeniería Matemática, Centro de Modelamiento, Matemático UMR2071 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile aut Vergara Ignacio Departamento de Ingeniería Matemática, Centro de Modelamiento, Matemático UMR2071 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1411-1428 1021-9722 22:5<1411 2015 22 30 https://doi.org/10.1007/s00030-015-0328-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0328-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Felmer Patricio Departamento de Ingeniería Matemática, Centro de Modelamiento, Matemático UMR2071 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile aut NATIONALLICENCE 700 1- Vergara Ignacio Departamento de Ingeniería Matemática, Centro de Modelamiento, Matemático UMR2071 CNRS-UChile, Universidad de Chile, Casilla 170 Correo 3, Santiago, Chile aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/5(2015-10-01), 1411-1428 1021-9722 22:5<1411 2015 22 30