Periodic and almost periodic results for some differential equations in Banach spaces. Ait Dads, E., Ezzinbi, K., & Arino, O. Nonlinear Anal., 31(1-2):163–170, 1998. 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)},
}
Downloads: 0
{"_id":"x2MMQgMXW54Ecee6P","bibbaseid":"aitdads-ezzinbi-arino-periodicandalmostperiodicresultsforsomedifferentialequationsinbanachspaces-1998","authorIDs":[],"author_short":["Ait Dads, E.","Ezzinbi, K.","Arino, O."],"bibdata":{"bibtype":"article","type":"article","author":[{"propositions":[],"lastnames":["Ait","Dads"],"firstnames":["E."],"suffixes":[]},{"propositions":[],"lastnames":["Ezzinbi"],"firstnames":["K."],"suffixes":[]},{"propositions":[],"lastnames":["Arino"],"firstnames":["Ovide"],"suffixes":[]}],"title":"Periodic and almost periodic results for some differential equations in Banach 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)","bibtex":"@Article{AitDadsEzzinbiArino1998,\r\n author = {Ait Dads, E. and Ezzinbi, K. and Arino, Ovide},\r\n title = {Periodic and almost periodic results for some differential equations in {B}anach spaces},\r\n journal = {Nonlinear Anal.},\r\n year = {1998},\r\n volume = {31},\r\n number = {1-2},\r\n pages = {163--170},\r\n issn = {0362-546X},\r\n abstract = {The main result is an extension of recent results of\r\n Kato and Imai [same journal, 24 (1995), 1183-1192\r\n and 25 (1995), 409-411]. It is shown that under\r\n certain hypotheses, an equation of the form $x'(t) =\r\n A(t, x(t)) + f(t)$ has a unique bounded solution\r\n that is almost periodic. The hypotheses include\r\n regularity assumptions on $A$ and $f$ and a\r\n dissipativity condition on $A$. The techniques used\r\n allow the proof to work for $x(t)$ taking on values\r\n in a Banach space (the earlier results required a\r\n Hilbert space), and the required dissipativity\r\n condition is less restrictive than with the earlier\r\n results.},\r\n classmath = {*34G99 ODE in abstract spaces },\r\n coden = {NOANDD},\r\n fjournal = {Nonlinear Analysis. Theory, Methods \\& Applications. An International Multidisciplinary Journal},\r\n mrclass = {34G20 (34C25 34C27)},\r\n mrnumber = {98j:34116},\r\n mrreviewer = {A. I. Perov},\r\n pdf = {AitDadsEzzinbiArino-1998-NATMA31.pdf},\r\n reviewer = {Mike Hurley (Cleveland)},\r\n}\r\n\r\n","author_short":["Ait Dads, E.","Ezzinbi, K.","Arino, O."],"key":"AitDadsEzzinbiArino1998","id":"AitDadsEzzinbiArino1998","bibbaseid":"aitdads-ezzinbi-arino-periodicandalmostperiodicresultsforsomedifferentialequationsinbanachspaces-1998","role":"author","urls":{},"downloads":0},"bibtype":"article","biburl":"https://server.math.umanitoba.ca/~jarino/ovide/papers/BiblioOvide.bib","creationDate":"2019-12-20T14:16:41.187Z","downloads":0,"keywords":[],"search_terms":["periodic","periodic","results","differential","equations","banach","spaces","ait dads","ezzinbi","arino"],"title":"Periodic and almost periodic results for some differential equations in Banach spaces","year":1998,"dataSources":["DJzjnMX7p3giiS766"]}