Existence and exponential decay of ground-state solutions for a nonlinear Dirac equation

被引：12
|
作者：
Zhang, Jian [1 ,2 ]
Zhang, Wen [1 ,2 ,3 ]
Zhao, Fukun [4 ]
机构：
[1] Hunan Univ Commerce, Sch Math & Stat, Changsha 410205, Hunan, Peoples R China
[2] Hunan Univ Commerce, Key Lab Hunan Prov New Retail Virtual Real Techno, Changsha 410205, Hunan, Peoples R China
[3] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
[4] Yunnan Normal Univ, Dept Math, Kunming 650500, Yunnan, Peoples R China
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2018年 / 69卷 / 05期
关键词：
Dirac equation; Ground-state solutions; Periodic and asymptotically periodic; Variational methods; INDEFINITE LINEAR PART; SCHRODINGER-EQUATIONS; STATIONARY STATES; CRITICAL GROWTH; POTENTIALS; FIELD; INFINITY;
D O I：
10.1007/s00033-018-1009-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the following nonlinear Dirac equation -i Sigma(3)(k=1) alpha(k)partial derivative(k)u+ a beta u + V (x)u = f (x,vertical bar u vertical bar) u, x is an element of R-3. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. Under some suitable conditions on the potential and nonlinearity, we obtain the existence of ground-state solutions in periodic case and asymptotically periodic case via variational methods, respectively. Moreover, we also explore some properties of these ground-state solutions, such as compactness of set of ground-state solutions and exponential decay of ground-state solutions.
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页数：23
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