Resumen de Concentrating solutions for a class of nonlinear fractional Schrödinger equations in RN

Vincenzo Ambrosio

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

  ε2s(−Δ)su+V(x)u=f(u)in RN, where ε>0 is a parameter, s∈(0,1), N≥2, (−Δ)s is the fractional Laplacian operator, and V:RN→R is a positive continuous function. Under the assumptions that the nonlinearity f 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 V as ε tends to zero.