On the topological structure of almost automorphic and asymptotically almost automorphic solutions of differential and integral equations in abstract spaces |
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| Affiliation: | 1. Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland;2. Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA;1. Cadi Ayyad University, LIBMA, B.P. 2390, Marrakesh, Morocco;2. Le Mans Université, LMM, Avenue Olivier Messiaen - 72085 Le Mans, France;1. Department of Mathematics, VNU University of Education, Vietnam National University at Hanoi, Hanoi, Viet Nam;2. Division of Mathematics, Truong THPT Trung Van, Phuong Trung Van, Nam Tu Liem, Hanoi, Viet Nam;3. Department of Mathematics and Statistics, University of Arkansas at Little Rock, 2801 S University Ave, Little Rock, AR 72204, USA;1. Université Ibn Zohr d׳Agadir, Maroc, Faculty of Sciences, Laboratory of Applied Mathematics and Applications (Functional Analysis Group). BP. 8106, Cité Dakhla, Agadir Maroc, France;2. Université de Lyon, F-69003, France;3. Université Lyon 1, CNRS UMR 5007, Laboratory of Process Control and Chemical Engineering (LAGEP), 43 bd du 11 novembre, 69100 Villeurbanne, France;1. Department of Mathematics and Computer Science, University of Perugia, Italy;2. Department of Mathematics and Informatics “Ulisse Dini”, University of Florence, Italy |
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| Abstract: | The main purpose of this paper is to deal with almost automorphic and asymptotically almost automorphic solutions of the initial value problem as well as the nonlinear Volterra integral equation in Banach spaces. We obtain a collection of existence results of such solutions to these equations. We investigate also a topological structure of such solution sets. Moreover, we prove Aronszajn-type theorems for solutions of the initial value problem as well as the nonlinear Volterra integral equation, defined on the whole real line. |
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