Bound state for fractional Schrodinger equation with saturable nonlinearity

In this paper, we study the existence of bound state for the following fractional Schrodinger equation (-Delta)(alpha)u + V(x)u = f(u), x is an element of R-N, N >= 3, where (-Delta)(alpha) with alpha is an element of (0,1) is the fractional Laplace operator defined as a pseudo-differential operator with the symbol vertical bar xi vertical bar(2 alpha), V(x) is a positive potential function and the nonlinearity f is saturable, that is, f(u)/u -> l is an element of (0,+infinity) as vertical bar u vertical bar -> +infinity. By using a variant version of Mountain Pass Theorem, we prove that there exists a bound state and ground state of (P) when V and f satisfy suitable assumptions. (C) 2015 Elsevier Inc. All rights reserved.