Existence and multiplicity of positive solutions for fractional Schrödinger equations with critical growth. (June 2017) - Tao, Fei; Wu, Xian
Abstract: In this paper, we study the existence and multiplicity of positive solutions for the fractional Schrödinger equations ε 2 α ( − Δ ) α u + V ( x ) u = ∣ u ∣ 2 α ∗ − 2 u + σ g ( x, u ), x ∈ R N, where ε and σ are positive parameters, 0 < α < 1, ( − Δ ) α denotes the fractional Laplacian of order α, N > 2 α and 2 α ∗ = 2 N N − 2 α is the fractional critical exponent, V ∈ C ( R N, R + ), g ∈ C ( R N × 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).