On almost automorphic type solutions of abstract integral equations, a Bohr-Neugebauer type property and some applications
Chávez A., Pinto M., Zavaleta U. · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) · 2021
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.