EXISTENCE AND CONCENTRATION OF POSITIVE SOLUTIONS FOR A FRACTIONAL LOGARITHMIC SCHRODINGER EQUATION

In this paper, by using the variational methods, we study the existence and concentration of positive solutions for the following fractional logarithmic Schrodinger equation epsilon(2s) (-Delta)(s)u V(x)u = u log u(2) , x is an element of R-N, where epsilon > 0 is a parameter, N > 2s, s is an element of (0,1) and (-Delta)(s) is the fractional Laplacian, the potential V : R-N -> R is a continuous function satisfying a local assumption. We generalize the result obtained by Alves and Ji [3] for the case s = 1 to the fractional logarithmic Schrodinger equation.