Existence and multiplicity of positive solutions for fractional Schrödinger equations with critical growth. (June 2017)

• Record Type: Journal Article
• Authors: Tao, Fei; Wu, Xian
• Is Part Of: Nonlinear analysis. Volume 35(2017)
• Page Start: 158
• Page End: 174
• Publication Date: 2017-06
• Subjects: Fractional Schrödinger equations -- Ground state solutions -- Variational methods; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.10.007
• Languages: English
• ISSNs: 1468-1218

Abstract

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).