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Browsing by Subject "solutions with a constant sign"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    On the asymptotic behaviour of solutions to a linear functional equation
    (2012) Sokołowski, Dariusz
    We investigate the asymptotic behaviour at infinity of solutions of the equation $\varphi (x) = \int_S \varphi (x+M(s))\sigma(d s).$ We show among others that, under some assumptions, any positive solution of the equation which is integrable on a vicinity of infinity or vanishes at $+\infty$ tends on some sequence to zero faster than some exponential function, but it does not vanish faster than another such function.