Existence of S-asymptotically ω-periodic solutions to abstract integro-differential equations

José Paulo Carvalho dos Santos and Hernán R. Henríquez

Applied Mathematics and Computation, 2015, vol. 256, issue C, 109-118

Abstract: The main aim of this work is to study the existence of S-asymptotically ω-periodic solutions for a class of abstract integro-differential equations modeled in the following formddt[x(t)+∫0tN(t-s)x(s)ds]=Ax(t)+∫0tB(t-s)x(s)ds+f(t,x(t)),t⩾0,x(0)=x0∈X,where A,B(t) for t⩾0 are closed linear operators defined on a common domain D(A) which is dense in X,N(t) for t⩾0 are bounded linear operators on X, and f:[0,∞)×X→X is an appropriate function. The existence results are obtained by applying the theory of exponentially stable resolvent operators. We also discuss an application of these results.

Keywords: Integro-differential equations; Abstract differential equations; S-asymptotically ω-periodic solutions; Mild solutions; Resolvent operator (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:256:y:2015:i:c:p:109-118

DOI: 10.1016/j.amc.2015.01.005

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