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. 1367–1414DOI 10.4171/RMI/1086