Existence of positive ground state solutions for fractional Schrödinger equations with a general nonlinearity. Issue 7 (19th May 2018)

• Record Type: Journal Article
• Authors: Liu, Zhisu; Ouyang, Zigen
• Is Part Of: Applicable analysis. Volume 97:Issue 7(2018)
• Page Start: 1154
• Page End: 1171
• Publication Date: 2018-05-19
• Subjects: Fractional Schrödinger equation -- ground state solution -- variational method -- global compactness lemma; 35J50 -- 35B38 -- 35J65; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1307963
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study the existence of positive ground state solutions for the nonlinear fractional Schrödinger equation: ( - ▵ ) α u + V ( x ) u = f ( u ), in R N, where N ≥ 2, α ∈ ( 0, 1 ), f ∈ C 1 ( R, R ) is subcritical near infinity and superlinear near zero and satisfies the Berestycki–Lions condition. Using the monotonic trick established by Struwe–Jeanjean, the method of Pohozaev manifold and establishing a global compactness lemma, we show that the above problem has at least a positive ground state solution.