abstract bibtex

The main result is an extension of recent results of Kato and Imai [same journal, 24 (1995), 1183-1192 and 25 (1995), 409-411]. It is shown that under certain hypotheses, an equation of the form $x'(t) = A(t, x(t)) + f(t)$ has a unique bounded solution that is almost periodic. The hypotheses include regularity assumptions on $A$ and $f$ and a dissipativity condition on $A$. The techniques used allow the proof to work for $x(t)$ taking on values in a Banach space (the earlier results required a Hilbert space), and the required dissipativity condition is less restrictive than with the earlier results.

@Article{AitDadsEzzinbiArino1998, author = {Ait Dads, E. and Ezzinbi, K. and Arino, Ovide}, title = {Periodic and almost periodic results for some differential equations in {B}anach spaces}, journal = {Nonlinear Anal.}, year = {1998}, volume = {31}, number = {1-2}, pages = {163--170}, issn = {0362-546X}, abstract = {The main result is an extension of recent results of Kato and Imai [same journal, 24 (1995), 1183-1192 and 25 (1995), 409-411]. It is shown that under certain hypotheses, an equation of the form $x'(t) = A(t, x(t)) + f(t)$ has a unique bounded solution that is almost periodic. The hypotheses include regularity assumptions on $A$ and $f$ and a dissipativity condition on $A$. The techniques used allow the proof to work for $x(t)$ taking on values in a Banach space (the earlier results required a Hilbert space), and the required dissipativity condition is less restrictive than with the earlier results.}, classmath = {*34G99 ODE in abstract spaces }, coden = {NOANDD}, fjournal = {Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal}, mrclass = {34G20 (34C25 34C27)}, mrnumber = {98j:34116}, mrreviewer = {A. I. Perov}, pdf = {AitDadsEzzinbiArino-1998-NATMA31.pdf}, reviewer = {Mike Hurley (Cleveland)}, }

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