Multiplicity of Normalized Solutions to a Fractional Logarithmic Schrodinger Equation

We study the existence and multiplicity of normalized solutions to the fractional logarithmic Schrodinger equation (-Delta)(s)u + V(epsilon x)u = lambda u + u log u(2) in R-N, under the mass constraint integral(N)(R) |u|(2)dx = a. Here, N >= 2, a, epsilon > 0, lambda is an element of R is an unknown parameter, (-Delta)(s) is the fractional Laplacian and s is an element of (0,1). We introduce a function space where the energy functional associated with the problem is of class C-1. Then, under some assumptions on the potential V and using the Lusternik-Schnirelmann category, we show that the number of normalized solutions depends on the topology of the set for which the potential V reaches its minimum.