Stable manifolds for impulsive delay equations and parameter dependence
Date
2019-02-13
Authors
Bahuguna, Dhirendra
Singh, Lokesh
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In this article, we establish the existence of Lipschitz stable invariant manifolds for the semiflows generated by the delay differential equation x′ = L(t)xt + ƒ(t, xt, λ) with impulses at times {τi}∞i=1, assuming that the perturbation ƒ(t, xt, λ) as well as the impulses are small and the corresponding linear delay differential equation admits a nonuniform exponential dichotomy. We also show that the obtained manifolds are Lipschitz in the parameter λ.
Description
Keywords
Delay impulsive equation, Exponential dichotomy, Stable invariant manifold
Citation
Bahuguna, D., & Singh, L. (2019). Stable manifolds for impulsive delay equations and parameter dependence. <i>Electronic Journal of Differential Equations, 2019</i>(25), pp. 1-22.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.