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.

Rights License