文摘
In this paper, we study the existence and multiplicity of positive solutions for the fractional Schrödinger equations ε2α(−Δ)αu+V(x)u=∣u∣2α∗−2u+σg(x,u),x∈RN, where εε and σσ are positive parameters, 0<α<10<α<1, (−Δ)α denotes the fractional Laplacian of order αα, N>2αN>2α and 2α∗=2NN−2α is the fractional critical exponent, V∈C(RN,R+)V∈C(RN,R+), g∈C(RN×R,R)g∈C(RN×R,R). By the variational methods we study the existence and multiplicity of positive solutions. Our main results improve corresponding results in Shang and Zhang (2014).