The concentration behavior of ground state solutions for nonlinear Dirac equation. (June 2020)

• Record Type: Journal Article
• Authors: Ding, Yanheng; Yu, Yuanyang
• Is Part Of: Nonlinear analysis. Volume 195(2020)
• Publication Date: 2020-06
• Subjects: 35Q40 -- 49J35; Nonlinear Dirac equation -- Ground state solutions -- Concentration; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.111738
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the following nonlinear Dirac equation − i ε ∑ k = 1 3 α k ∂ k u + a β u + V ( x ) u = K ( x ) f ( | u | ) u, in R 3, where ε > 0 is a small parameter, a > 0 is a constant, α 1, α 2, α 3 and β are 4 × 4 Pauli–Dirac matrices, V, K and f are continuous but are not necessarily of class C 1 . We prove the existence of ground state solution by using variational methods, and we determine a concrete set related to the potentials V and K as the concentration position of these ground state solutions as ε → 0 . Moreover, we consider some properties of these ground state solutions, such as convergence and exponential decay estimate. The result presented in this paper generalizes the result in Ding and Liu (2012).