# American Institute of Mathematical Sciences

March  2016, 15(2): 457-475. doi: 10.3934/cpaa.2016.15.457

## Competing interactions and traveling wave solutions in lattice differential equations

 1 Department of Mathematics, University of Kansas, Lawrence, KS 66045, United States 2 Department of Mathematical Sciences, University of Arkansas, Fayetteville, AR 72701, United States

Received  March 2015 Revised  November 2015 Published  January 2016

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 [1], 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.
Citation: E. S. Van Vleck, Aijun Zhang. Competing interactions and traveling wave solutions in lattice differential equations. Communications on Pure & Applied Analysis, 2016, 15 (2) : 457-475. doi: 10.3934/cpaa.2016.15.457
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