Normalized solutions for the fractional Schrodinger equation with combined nonlinearities

In this paper, we study the normalized solutions for the following fractional Schrodinger equation with combined nonlinearities {(-Delta)(s) u=lambda u + mu vertical bar u vertical bar(q-2)u+ vertical bar u vertical bar(p-2)u in R-N, integral(RN) u(2) dx = a(2), where 0 < s < 1, N > 2s, 2 < q < p = 2(s)* = 2N/N-2, a, mu > 0 and lambda is an element of R is a Lagrange multiplier. Since the existence results for p < 2(s)* have been proved, using an approximation method, that is, let p -> 2(s)*, we obtain several existence results. Moreover, we analyze the asymptotic behavior of solutions as mu -> 0 and mu goes to its upper bound.