Almost automorphic delayed differential equations and Lasota-Wazewska model

Coronel, Aníbal; Maulén, Christopher; Pinto, Manuel; Sepúlveda, Daniel

doi:10.3934/dcds.2017083

Cited by 10 publications

(5 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we study the following model: y (t) = -δy(t) + h(t)e -a(t)y(t-τ ) , t ≥ 0, (4.2) where τ > 0, h(t) and a(t) are continuous and positive functions. Equation (42) models several situations in the real life, see, for example, [7,8,11,18] and the references therein. We are looking for positive (ω, c)-pseudo periodic solutions for certain ω > 0, c > 0.…”

Section: Lasota-wazewska Model With Unbounded Oscillating and Ergodicmentioning

confidence: 99%

$(\omega ,c)$-Pseudo periodic functions, first order Cauchy problem and Lasota–Wazewska model with ergodic and unbounded oscillating production of red cells

2019

Self Cite

View full text Add to dashboard Cite

In this paper we study a new class of functions, which we call (ω, c)-pseudo periodic functions. This collection includes pseudo periodic, pseudo anti-periodic, pseudo Bloch-periodic, and unbounded functions. We prove that the set conformed by these functions is a Banach space with a suitable norm. Furthermore, we show several properties of this class of functions as the convolution invariance. We present some examples and a composition result. As an application, we prove the existence and uniqueness of (ω, c)-pseudo periodic mild solutions to the first order abstract Cauchy problem on the real line. Also, we establish some sufficient conditions for the existence of positive (ω, c)-pseudo periodic solutions to the Lasota-Wazewska equation with unbounded oscillating production of red cells.

show abstract

Section: Lasota-wazewska Model With Unbounded Oscillating and Ergodicmentioning

confidence: 99%

$(\omega ,c)$-Pseudo periodic functions, first order Cauchy problem and Lasota–Wazewska model with ergodic and unbounded oscillating production of red cells

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section, we study the following model:

y^{'} false(t false) = - δ y false(t false) + h false(t false) e^{- a false(t false) y false(t - τ false)}, t \geq 0,

where τ >0, h ( t ) and a ( t ) are continuous and positive functions. Equation models several situations in the real life, see, for example, previous studies and the references therein. We are looking for positive ( ω , c )‐asymptotically periodic solutions for certain ω >0, c >0.…”

Section: Lasota‐wazewska Model With Unbounded Oscillating Production mentioning

confidence: 99%

(ω,c)‐asymptotically periodic functions, first‐order Cauchy problem, and Lasota‐Wazewska model with unbounded oscillating production of red cells

Álvarez

Castillo

Pinto³

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In this paper, we study a new class of functions, which we call ( , c)-asymptotically periodic functions. This collection includes asymptotically periodic, asymptotically antiperiodic, asymptotically Bloch-periodic, and unbounded functions. We prove that the set conformed by these functions is a Banach space with a suitable norm. Furthermore, we show several properties of this class of functions as the convolution invariance. We present some examples and a composition result. As an application, we prove the existence and uniqueness of ( , c)-asymptotically periodic mild solutions to the first-order abstract Cauchy problem on the real line. Also, we establish some sufficient conditions for the existence of positive ( , c)-asymptotically periodic solutions to the Lasota-Wazewska equation with unbounded oscillating production of red cells.

show abstract

“…In [8], the author remark that in the context of almost automorphic differential equations the Bialmost automorphic (abbrev. as Bi-a.a.) property of the Green function is fundamental to prove the existence of solution of the same class.…”

Section: Introductionmentioning

confidence: 99%

Pseudo compact almost automorphic solutions to a family of non-monotone delayed differential equations

Zheng

2022

Preprint

View full text Add to dashboard Cite

In this paper, a family of non-monotone differential equations with mixed delays is considered. By introducing a concept of Bi-pseudo compact almost automorphic functions and establishing the properties of these functions, and using Halanay’s inequality and Banach fixed point theorem, some results on the existence, uniqueness and global exponential stability of pseudo compact automorphic solutions of the equations are obtained. Our results extend some recent works. Moreover, an example is given to illustrate the validity of our results.

show abstract

Almost automorphic delayed differential equations and Lasota-Wazewska model

Cited by 10 publications

References 46 publications

$(\omega ,c)$-Pseudo periodic functions, first order Cauchy problem and Lasota–Wazewska model with ergodic and unbounded oscillating production of red cells

$(\omega ,c)$-Pseudo periodic functions, first order Cauchy problem and Lasota–Wazewska model with ergodic and unbounded oscillating production of red cells

(ω,c)‐asymptotically periodic functions, first‐order Cauchy problem, and Lasota‐Wazewska model with unbounded oscillating production of red cells

Pseudo compact almost automorphic solutions to a family of non-monotone delayed differential equations

Contact Info

Product

Resources

About