Stable manifolds for impulsive delay equations and parameter dependence
Year: 2019
Type: article
Abstract: In this article, we establish the existence of Lipschitz stable invariant manifolds for the semiflows generated by the delay differential equation $x'= L(t)x_t + f(t,x_t,\lambda)$ with impulses at times $\{\tau_i\}_{i=1}^\infty $, assuming that the perturbation $f(t,x_t,\lambda)$ 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 $\lambda$.
Authors: Dhirendra Bahuguna, Lokesh Singh
Institution: Indian Institute of Technology Kanpur
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4407097293