arXiv subjects

Hernán R. Henríquez

Publications and source records attributed to Hernán R. Henríquez.

3 recordsLinked to original sources

arXiv2026

Controllability of time-varying lumped semilinear systems

In this work we are concerned with the controllability of time-varying lumped control systems governed by a semilinear differential equation. We consider the semilinear system as a perturbation of a linear system. Assuming the underlying linear system is controllable, and the nonlinear forcing function satisfies a boundedness condition which is adapted to the underlying linear system, we show that the semilinear system is also approximately controllable

math.OC↗

arXiv2026

Evolution families and variation of constants formula for abstract functional differential equations with time-dependent infinite delay

In this paper, we consider a class of first-order abstract retarded functional differential equations in Banach spaces, incorporating a time-dependent infinite delay governed by a regulated function. We establish the existence of mild solutions for the nonlinear equation and show that the family of solution maps for the linear equation forms a well-defined evolution family of bounded linear operators on an appropriate phase space. Furthermore, we leverage this evolution family to prove a variation of constants formula for the inhomogeneous linear problem.

math.CA↗

arXiv2022

Hybrid measure differential equations: existence of solutions and continuous dependence on parameters

This paper is devoted to study the qualitative properties of hybrid measure differential equations (HMDEs, for short). We establish several results on the existence of global solutions, including the existence of regulated, continuous, differentiable and S-asymptotically $ω$-periodic solutions. Furthermore, we present a result on continuous dependence of solutions in terms of parameters. Our results are based on extensions of Kasnoselskii's fixed-point theorem.

math.CA↗