On almost automorphic type solutions of abstract integral equations, a Bohr-Neugebauer type property and some applications

• Autores: Chávez A., Pinto M., Zavaleta U.
• Formato: artículo
• Fecha de Publicación: 2021
• Institución: Consejo Nacional de Ciencia Tecnología e Innovación
• Repositorio: CONCYTEC-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.concytec.gob.pe:20.500.12390/2395
• Enlace del recurso: https://hdl.handle.net/20.500.12390/2395; https://doi.org/10.1016/j.jmaa.2020.124395
• Nivel de acceso: acceso abierto
• Materia: Mild solutions; Abstract integral equations; Almost automorphic functions; Asymptotically almost automorphic functions; Bohr-Neugebauer property; http://purl.org/pe-repo/ocde/ford#1.01.01

In the present work we give some sufficient conditions to obtain a unique almost automorphic solution to abstract nonlinear integral equations which are simultaneously of advanced and delayed type and also a unique asymptotically almost automorphic mild solution to abstract integro-differential equations with nonlocal initial conditions, both situations are posed on Banach spaces. Also, we develop a Bohr-Neugebauer type result for the abstract integral equations. Before that, we introduce the notion of ?-bounded functions, develop the appropriate abstract theory and discuss the almost periodic situation. As applications, we study the existence of an asymptotically almost automorphic solution to integro-differential equations modeling heat conduction in materials with memory and also the existence of the almost automorphic solution to semilinear parabolic evolution equations with finite delay. © 2020 Elsevier Inc.