Abstract
In this paper, an investigation is initiated of boundary-value problems for singularly perturbed linear second-order differential-difference equations with small shifts, i.e., where the second-order derivative is multiplied by a small parameter and the shift depends on the small parameter. Similar boundary-value problems are associated with expected first-exit times of the membrane potential in models for neurons. In particular, this paper focuses on problems with solutions that exhibit layer behavior at one or both of the boundaries. The analyses of the layer equations using Laplace transforms lead to novel results. It is shown that the layer behavior can change its character and even be destroyed as the shifts increase but remain small. In the companion paper [SIAM J. Appi. Math., 54 (1994), pp. 273–283], similar boundary-value problems with solutions that exhibit rapid oscillations are studied.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
