Concentrating solutions for a class of nonlinear fractional Schrödinger equations in

  • Vincenzo Ambrosio

    Università Politecnica delle Marche, Ancona, Italy
Concentrating solutions for a class of nonlinear fractional Schrödinger equations in $\mathbb R^N$ cover

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Abstract

We deal with the existence of positive solutions for the following fractional Schrödinger equation:

where is a parameter, , , is the fractional Laplacian operator, and is a positive continuous function. Under the assumptions that the nonlinearity is either asymptotically linear or superlinear at infinity, we prove the existence of a family of positive solutions which concentrates at a local minimum of as tends to zero.

Cite this article

Vincenzo Ambrosio, Concentrating solutions for a class of nonlinear fractional Schrödinger equations in . Rev. Mat. Iberoam. 35 (2019), no. 5, pp. 1367–1414

DOI 10.4171/RMI/1086