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Asymptotically almost periodic solutions to some classes of second-order functional differential equations. (English) Zbl 1224.35411

Summary: In this paper we study the existence of asymptotically almost periodic solutions to some classes of second-order partial functional-differential equations with unbounded delay. Our results are, subsequently, applied to studying the existence of asymptotically almost periodic solutions to some integro-differential equations, which arise in the theory of heat conduction within fading memory materials.

MSC:

35R10 Partial functional-differential equations
35B15 Almost and pseudo-almost periodic solutions to PDEs
34K30 Functional-differential equations in abstract spaces
43A60 Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
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