On fractional Schrödinger equations with Hartree type nonlinearities

Silvia Cingolani*, Marco Gallo, Kazunaga Tanaka

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Goal of this paper is to study the following doubly nonlocal equation (equation presented) in the case of general nonlinearities F 2 C1(R) of Berestycki-Lions type, when N ≥ 2 and μ > 0 is fixed. Here (-Δ)s, s ∈(0; 1), denotes the fractional Laplacian, while the Hartree-type term is given by convolution with the Riesz potential Iα, α 2 (0; N). We prove existence of ground states of (P). Furthermore we obtain regularity and asymptotic decay of general solutions, extending some results contained in [23, 61].

Original languageEnglish
Pages (from-to)1-33
Number of pages33
JournalMathematics In Engineering
Volume4
Issue number6
DOIs
Publication statusPublished - 2022 Jan 1

Keywords

  • Asymptotic decay
  • Choquard nonlinearity
  • Double nonlocality
  • Fractional Laplacian
  • Hartree term
  • Nonlinear Schr odinger equation
  • Regularity
  • Symmetric solutions

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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