Electron. J. Differential Equations, Vol. 2025 (2025), No. 91, pp. 1-19.
Compact almost automorphic dynamics of linear non-autonomous differential equations
with exponential dichotomy and of delayed biological models
Alan Chavez, Nelson Aragones, Ulices Zavaleta, Manuel Pinto
Abstract:
In this work, we study the dynamics of linear non-autonomous differential equations
with exponential dichotomy and compact almost automorphic perturbations.
First, we prove that if the homogeneous system is exponentially dichotomous and the
coefficient matrix is compact almost automorphic, then the associated Green's function
is compact bi-almost automorphic and uniformly continuous relative to the principal
diagonal of the two-dimensional Euclidean space. Next, we demonstrate the invariance
of the compact almost automorphic function space under convolution products with
Green's function as the kernel. These results ensures that the unique bounded solution
of a linear non-autonomous differential equation, under exponential dichotomy and with
compact almost automorphic perturbation, is itself compact almost automorphic.
Finally, we investigate the existence and the global exponential stability of a
unique positive compact almost automorphic solution for a nonlinear non-autonomous
delayed biological model with nonlinear harvesting or immigration terms and mixed delays.
Submitted May 7, 2025. Published September 2, 2025.
Math Subject Classifications: 34A30, 34A34, 34C27, 34K14, 35B99.
Key Words: Compact almost automorphic functions; bi-almost automorphic functions; non-autonomous differential systems; exponential dichotomy; biological models.
DOI: 10.58997/ejde.2025.91
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Alan Chávez
OASIS and GRACOCC Research Groups
Instituto de investigación en Matemáticas
Departamento de Matemáticas, FCFYM
Universidad Nacional de Trujillo
Av. Juan Pablo II S/N, Trujillo, Perú
email: ajchavez@unitru.edu.pe
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Nelson Aragonés
OASIS Research Group
Departamento de Matemáticas, FCFYM
Universidad Nacional de Trujillo
Av. Juan Pablo II S/N, Trujillo, Perú
email: naragones@unitru.edu.pe
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Ulices Zavaleta
OASIS Research Group
Instituto de investigación en Matemáticas
Departamento de Matemáticas, FCFYM
Universidad Nacional de Trujillo
Av. Juan Pablo II S/N, Trujillo, Perú
email: auzavaleta@unitru.edu.pe
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Manuel Pinto
Departamento de Matemáticas
Facultad de Ciencias, Universidad de Chile
Las Palmeras 3425, Ñuñoa Santiago, Chile
email: pintoj.uchile@gmail.com
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