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Asymptotic periodicity and almost automorphy for a class of Volterra integro-differential equations. (English) Zbl 1243.45015

The existence of asymptotically periodic (resp. asymptotically almost automorphic) solutions for a class of Volterra integro-differential equations of the form \[ u'(t)=Au(t)+\int_o^{t}B(t-s)u(s)ds+ g(t,u(t), ~t\geq 0, \] is studied. An application to an equation arising in the study of heat conduction in materials with memory is presented.

MSC:

45J05 Integro-ordinary differential equations
45M05 Asymptotics of solutions to integral equations
45D05 Volterra integral equations
45G10 Other nonlinear integral equations
45M15 Periodic solutions of integral equations
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