Nodal bound state of nonlinear problems involving the fractional Laplacian. (19th June 2017)

• Record Type: Journal Article
• Authors: Long, Wei; Lv, Longbo
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 18(2018)
• Page Start: 6495
• Page End: 6509
• Publication Date: 2017-06-19
• Subjects: fractional Laplacian -- nonlinear Schrödinger equation -- reduction method; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4470
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper is concerned with the following nonlinear fractional Schrödinger equation ε 2 s ( − Δ ) s u + V ( x ) u = | u | p − 2 u, in R N, where ε >0 is a small parameter, V ( x ) is a positive function, 0< s <1, and 2 < p < 2 N N − 2 s ( N > 2 s ) . Under some suitable conditions, we prove that for any positive integer k, one can construct a nonradial sign‐changing (nodal) solutions with exactly k maximum points and k minimum points near the local minimum point of V ( x ).