Year: 2012
Author: Linghai Zhang, Melissa Anne Stoner
Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 4 : pp. 295–329
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v25.n4.1
Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 4 : pp. 295–329
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Nonhomogeneous synaptically coupled neuronal networks