TY - JOUR
T1 - Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks
AU - Zhang , Linghai
AU - Stoner , Melissa Anne
JO - Journal of Partial Differential Equations
VL - 4
SP - 295
EP - 329
PY - 2012
DA - 2012/12
SN - 25
DO - http://doi.org/10.4208/jpde.v25.n4.1
UR - https://global-sci.org/intro/article_detail/jpde/5188.html
KW - Nonhomogeneous synaptically coupled neuronal networks
KW - standing wave solutions
KW - existence
KW - stability
KW - eigenvalue problems
KW - Evans functions
AB - <p>The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed systemof integral differential equations and a nonlinear scalar integral differential equation. It will be shown that there exist six standing wave solutions (u(x,t),w(x,t))=(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations. Similarly, there exist six standing wave solutions u(x,t)=U(x) to the nonlinear scalar integral differential equation. The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.</p>