The concentration behavior of ground state solutions for nonlinear Dirac equation
Ding, Yanheng1; Yu, Yuanyang1,2
AbstractIn this paper, we study the following nonlinear Dirac equation -i epsilon Sigma(3)(k=1) alpha(k)partial derivative(k)u + alpha beta u + V(x)u =K(x)f(vertical bar u vertical bar)u, in R-3, where epsilon > 0 is a small parameter, a > 0 is a constant, alpha(1), alpha(2), alpha(3) and beta are 4 x 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 epsilon -> 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). (C) 2019 Elsevier Ltd. All rights reserved.
KeywordNonlinear Dirac equation Ground state solutions Concentration
Indexed BySCI
Funding ProjectNational Science Foundation of China[NSFC11871242]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000522150400039
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Document Type期刊论文
Corresponding AuthorYu, Yuanyang
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Ding, Yanheng,Yu, Yuanyang. The concentration behavior of ground state solutions for nonlinear Dirac equation[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2020,195:24.
APA Ding, Yanheng,&Yu, Yuanyang.(2020).The concentration behavior of ground state solutions for nonlinear Dirac equation.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,195,24.
MLA Ding, Yanheng,et al."The concentration behavior of ground state solutions for nonlinear Dirac equation".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 195(2020):24.
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