COMPETING INTERACTIONS AND TRAVELING WAVE SOLUTIONS IN LATTICE DIFFERENTIAL EQUATIONS

被引：1
|
作者：
Van Vleck, E. S. [1 ]
Zhang, Aijun [2 ]
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
[2] Univ Arkansas, Dept Math Sci, Fayetteville, AR 72701 USA
来源：
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2016年 / 15卷 / 02期
关键词：
Bistable; traveling waves; competing interaction; Fredholm operator; lattice differential equation; DISCRETE NAGUMO EQUATION; MIXED-TYPE; BISTABLE DYNAMICS; EXISTENCE; STABILITY; SYSTEMS; FRONTS;
D O I：
10.3934/cpaa.2016.15.457
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The existence of traveling front solutions to bistable lattice differential equations in the absence of a comparison principle is studied. The results are in the spirit of those in Bates, Chen, and Chmaj [I], but are applicable to vector equations and to more general limiting systems. An abstract result on the persistence of traveling wave solutions is obtained and is then applied to lattice differential equations with repelling first and/or second neighbor interactions and to some problems with infinite range interactions.
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页码：457 / 475
页数：19
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