• Korean Journal of Mathematics
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• v.28 no.2
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.635-644
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• 2010

We investigate the boundedness and asymptotic almost periodicity of solutions for discrete Volterra equations.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.417-427
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• 1994

Let C be a nonempty closed bounded convex subset of a real Banach space X.