Existence And Multiplicity Of Positive Solutions Forfractional Schrodinger Equations With Critical Growth

In this paper, we study the existence and multiplicity of solutions for the following fractional Schrodinger equations ε2α(-△)αu+V(x)u=|u|2*α-2u+σg(x,u), x ∈ RN, where ε and a are positive parameters,0< α< 1, (-△)α denotes the fractional Laplacian of order a, N> 2a and 2*α = 2N/N-2α is the fractional critical exponent, V ∈ C(RN,R+), g ∈ C(RN × R,R). We use the variational methods to relate the number of soltions with the topology of the set where V attains its minimum for all sufficiently large σ and small ε. Our main results improve corresponding results in [18] (X. Shang, J. Zhang, Gound states for fractional Schrodinger equations with critical growth, Nonlinearity,27(2014),187-207.)...