Ground state solutions for fractional scalar field equations under a general critical nonlinearity

2016/10/14 by Alves, Claudianor O., Figueiredo, Giovany M., Siciliano, Gaetano
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.04649

Abstract

In this paper we study existence of ground state solution to the following problem (- Δ)^αu = g(u) in ℝ^N, u ∈ H^α(\mathbb R^N) where (-Δ)^α is the fractional Laplacian, α∈ (0,1). We treat both cases N≥2 and N=1 with α=1/2. The function g is a general nonlinearity of Berestycki-Lions type which is allowed to have critical growth: polynomial in case N≥2, exponential if N=1.

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