Multiplicity of positive solutions for a class of fractional Schrodinger equations via penalization method

By using the penalization method and the Ljusternik-Schnirelmann theory, we investigate the multiplicity of positive solutions of the following fractional Schrodinger equation epsilon(2s) (-Lambda)(s) u + V(x)u = f (u) in R-N where epsilon > 0 is a parameter, s epsilon (0,1), N > 2s, (-Delta)(s) is the fractional Laplacian, V is a positive continuous potential with local minimum, and f is a superlinear function with subcritical growth. We also obtain a multiplicity result when f(u) = vertical bar u vertical bar(q-2) u + lambda vertical bar u vertical bar(r-2) u with 2 < q < 2(s)* <= r and lambda, by combining a truncation argument and a Moser-type iteration.