TY - JOUR

T1 - Controllability of semilinear neutral differential equations with impulses and nonlocal conditions

AU - Camacho, Oscar

AU - Leiva, Hugo

AU - Riera-Segura, Lenin

N1 - Publisher Copyright:
© 2022 John Wiley & Sons, Ltd.

PY - 2022/11/15

Y1 - 2022/11/15

N2 - When a real-life problem is mathematically modeled by differential equations or another type of equation, there are always intrinsic phenomena that are not taken into account and can affect the behavior of such a model. For example, external forces can abruptly change the model; impulses and delay can cause a breakdown of it. Considering these intrinsic phenomena in the mathematical model makes the difference between a simple differential equation and a differential equation with impulses, delay, and nonlocal conditions. So, in this work, we consider a semilinear nonautonomous neutral differential equation under the influence of impulses, delay, and nonlocal conditions. In this paper we study the controllability of these semilinear neutral differential equations with some of these intrinsic phenomena taking into consideration. Our aim is to prove that the controllability of the associated ordinary linear differential equation is preserved under certain conditions imposed on these new disturbances. In order to achieve our objective, we apply Rothe's fixed point Theorem to prove the exact controllability of the system. Finally, our method can be extended to the evolution equation in Hilbert spaces with applications to control systems governed by PDE's equations.

AB - When a real-life problem is mathematically modeled by differential equations or another type of equation, there are always intrinsic phenomena that are not taken into account and can affect the behavior of such a model. For example, external forces can abruptly change the model; impulses and delay can cause a breakdown of it. Considering these intrinsic phenomena in the mathematical model makes the difference between a simple differential equation and a differential equation with impulses, delay, and nonlocal conditions. So, in this work, we consider a semilinear nonautonomous neutral differential equation under the influence of impulses, delay, and nonlocal conditions. In this paper we study the controllability of these semilinear neutral differential equations with some of these intrinsic phenomena taking into consideration. Our aim is to prove that the controllability of the associated ordinary linear differential equation is preserved under certain conditions imposed on these new disturbances. In order to achieve our objective, we apply Rothe's fixed point Theorem to prove the exact controllability of the system. Finally, our method can be extended to the evolution equation in Hilbert spaces with applications to control systems governed by PDE's equations.

KW - controllability of neutral equations

KW - impulses

KW - nonlocal conditions

KW - rothe's fixed point theorem

KW - semilinear equations

UR - http://www.scopus.com/inward/record.url?scp=85129517764&partnerID=8YFLogxK

U2 - 10.1002/mma.8340

DO - 10.1002/mma.8340

M3 - Artículo

AN - SCOPUS:85129517764

SN - 0170-4214

VL - 45

SP - 9826

EP - 9839

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

IS - 16

ER -