Multiplicity and concentration of solutions for fractional Schrödinger systems via penalization method

  • Vincenzo Ambrosio

    Università Politecnica delle Marche, Ancona, Italy
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Abstract

The aim of this paper is to investigate the existence, multiplicity and concentration of positive solutions for the following nonlocal system of fractional Schrödinger equations

where is a parameter, , , is the fractional Laplacian, and are positive continuous potentials, is a homogeneous -function with subcritical growth. In order to relate the number of solutions with the topology of the set where the potentials and attain their minimum values, we apply penalization techniques, Nehari manifold arguments and Ljusternik–Schnirelmann theory.

Cite this article

Vincenzo Ambrosio, Multiplicity and concentration of solutions for fractional Schrödinger systems via penalization method. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 30 (2019), no. 3, pp. 543–581

DOI 10.4171/RLM/860