Electron. J. Differential Equations, Vol. 2017 (2017), No. 239, pp. 1-30.

Existence of generalized almost periodic and asymptotic almost periodic solutions to abstract Volterra integro-differential equations

Marko Kostic

The main aim of this paper is to study the asymptotic almost periodicity, Stepanov almost periodicity, and asymptotic Stepanov almost periodicity of various classes of regularized solution operator families appearing in the theory of abstract Volterra integro-differential equations. Subgenerators of these solution operator families, which can be degenerate or non-degenerate in time, are multivalued linear operators. We contemplate the results established by many other authors, providing also a great number of original contributions, illustrative examples and applications of our abstract results.

Submitted April 18, 2017. Published October 3, 2017.
Math Subject Classifications: 35B15, 47D03, 47D60, 47D62, 34G25.
Key Words: Volterra integro-differential equations; (a,k)-regularized C-resolvent; Stepanov almost periodic; asymptotic almost periodic; asymptotic Stepanov almost periodic.

Show me the PDF file (413 KB), TEX file for this article.

Marko Kostic
Faculty of Technical Sciences
University of Novi Sad
Trg D. Obradovica 6
21125 Novi Sad, Serbia
email: marco.s@verat.net

Return to the EJDE web page