This paper focuses on the following scalar field equation involving a fractional Laplacian:(− ) α u = g(u) in R N , where N 2, α ∈ (0, 1), (− ) α stands for the fractional Laplacian. Using some minimax arguments, we obtain a positive ground state under the general Berestycki-Lions type assumptions.

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Orbital and asymptotic stability for standing waves of a nonlinear Schrödinger equation with concentrated nonlinearity in dimension three This paper is devoted to a time-independent fractional Schrödinger equation of the formwhere N ≥ 2, s ∈ (0, 1), ( − ) s stands for the fractional Laplacian. We apply the variational methods to obtain the existence of ground state solutions when f(x, u) is asymptotically linear with respect to u at infinity. C 2013 AIP Publishing LLC. [http://dx.

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