In this paper we study existence of ground state solution to the following problem (−∆)αu = g(u) in RN, u ∈ Hα(RN) where (−∆)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.
Ground state solutions for fractional scalar field equations under a general critical nonlinearity
Siciliano, Gaetano
2016-01-01
Abstract
In this paper we study existence of ground state solution to the following problem (−∆)αu = g(u) in RN, u ∈ Hα(RN) where (−∆)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.File in questo prodotto:
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