Periodic functions related to the Gompertz difference equation

Cuchta, Tom; Wintz, Nick

doi:10.3934/mbe.2022407

Cited by 3 publications

(1 citation statement)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Difference equations are a very nice outlet to study some real-life models with a biological background. From our mathematical point of view, it may be an interesting task to relate almost periodic and almost automorphic functions with biological models in a similar direction as paper [43], which focuses on periodic functions. Moreover, the abstract outcomes of this study can be implemented on some particular models in real-life processes.…”

Section: Discussionmentioning

confidence: 99%

Almost Automorphic Solutions to Nonlinear Difference Equations

Kostić,

Koyuncuoğlu,

Fedorov

2023

Mathematics

View full text Add to dashboard Cite

In the present work, we concentrate on a certain class of nonlinear difference equations and propose sufficient conditions for the existence of their almost automorphic solutions. In our analysis, we invert an appropriate mapping and obtain the main existence outcomes by utilizing the contraction mapping principle. As the second objective of the manuscript, we reconsider one of the landmark results, namely the Bohr–Neugebauer theorem, in the qualitative theory of dynamical equations, and we investigate the relationship between the existence of almost automorphic solutions and the existence of solutions with a relatively compact range for the proposed difference equation type. Thus, we provide a discrete counterpart of the Bohr–Neugebauer theorem due to the almost automorphy notion under some technical conditions.

show abstract

Section: Discussionmentioning

confidence: 99%

Almost Automorphic Solutions to Nonlinear Difference Equations

Kostić,

Koyuncuoğlu,

Fedorov

2023

Mathematics

View full text Add to dashboard Cite

show abstract

Almost Automorphic Solutions to Nonlinear Difference Equations

Kostić,

Koyuncuoglu,

Fedorov

2023

Preprint

View full text Add to dashboard Cite

In this study, we focus on an abstract form of summation equations, which can be regarded as a particular class of nonlinear difference equations. We investigate sufficient conditions for the existence of discrete almost automorphic solutions by appealing to the fixed point theory and establish a linkage between the existence of discrete almost automorphic solutions and the existence of bounded solutions for the nonlinear difference equations in the spotlight. Consequentially, we propose a discrete counterpart of the Bohr-Neugebauer theorem for the qualitative theory of difference equations.

show abstract

A lemma on C ₀ -semigroups on time scales and approximate controllability of the heat dynamic equation

Bohner,

Duque,

Leiva

et al. 2024

Quaestiones Mathematicae

View full text Add to dashboard Cite

Periodic functions related to the Gompertz difference equation

Abstract: <abstract><p>We investigate periodicity of functions related to the Gompertz difference equation. In particular, we derive difference equations that must be satisfied to guarantee periodicity of the solution.</p></abstract>

Cited by 3 publications

References 18 publications

Almost Automorphic Solutions to Nonlinear Difference Equations

Almost Automorphic Solutions to Nonlinear Difference Equations

Almost Automorphic Solutions to Nonlinear Difference Equations

A lemma on C ₀ -semigroups on time scales and approximate controllability of the heat dynamic equation

Contact Info

Product

Resources

About

Periodic functions related to the Gompertz difference equation

Abstract: <abstract><p>We investigate periodicity of functions related to the Gompertz difference equation. In particular, we derive difference equations that must be satisfied to guarantee periodicity of the solution.</p></abstract>

Cited by 3 publications

References 18 publications

Almost Automorphic Solutions to Nonlinear Difference Equations

Almost Automorphic Solutions to Nonlinear Difference Equations

Almost Automorphic Solutions to Nonlinear Difference Equations

A lemma on C 0 -semigroups on time scales and approximate controllability of the heat dynamic equation

Contact Info

Product

Resources

About

A lemma on C ₀ -semigroups on time scales and approximate controllability of the heat dynamic equation