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arXiv · 1912.13048

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

Alan Chávez·Manuel Pinto·Ulices Zavaleta
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Abstract

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 $\lambda$-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.

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Alan Chávez, Manuel Pinto, Ulices Zavaleta. 2019-12-30. On almost automorphic type solutions of abstract Integral equations, a Bohr-Neugebauer type property and some applications. https://arxiv.org/abs/1912.13048

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