Pseudo almost periodic solutions for some differential equations in a Banach space. Ait Dads, E., Ezzinbi, K., & Arino, O. Nonlinear Anal., 28(7):1141–1155, 1997.
abstract   bibtex   
Differential equations of the form $$dx/dt =f\bigl(t,x(t) \bigr)$$ are considered. A very important question in many practical situations connected with this type of equation is to know if there exists a mean value of a bounded solution $x(t)$. By the mean value it is understood the limit $$\lim\sbT\to\infty (1/2T) \int\sp T\sb-T x(t)dt$$ if it exists. A generalization of the problem with values of pseudo-almost-periodic functions in a Banach space is proposed.
@Article{AitDadsEzzinbiArino1997,
  author     = {Ait Dads, E. and Ezzinbi, K. and Arino, Ovide},
  title      = {Pseudo almost periodic solutions for some differential equations in a {B}anach space},
  journal    = {Nonlinear Anal.},
  year       = {1997},
  volume     = {28},
  number     = {7},
  pages      = {1141--1155},
  issn       = {0362-546X},
  abstract   = {Differential equations of the form $$dx/dt
                  =f\bigl(t,x(t) \bigr)$$ are considered. A very
                  important question in many practical situations
                  connected with this type of equation is to know if
                  there exists a mean value of a bounded solution
                  $x(t)$. By the mean value it is understood the limit
                  $$\lim\sb{T\to\infty} (1/2T) \int\sp T\sb{-T}
                  x(t)dt$$ if it exists. A generalization of the
                  problem with values of pseudo-almost-periodic
                  functions in a Banach space is proposed.},
  classmath  = {*34C27 Almost periodic solutions of ODE 34G20 Nonlinear ODE in abstract spaces },
  coden      = {NOANDD},
  fjournal   = {Nonlinear Analysis. Theory, Methods \& Applications. An International Multidisciplinary Journal},
  keywords   = {almost periodic functions; pseudo-almost-periodic functions; asymptotic almost-periodic functions},
  mrclass    = {34G10 (34C27 47N20)},
  mrnumber   = {98d:34089},
  mrreviewer = {John R. Graef},
  reviewer   = {S.G.Zhuravlev (Moskva)},
}

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