@Article{Sokołowski2012,
author = "Sokołowski, Dariusz",
title = "On the asymptotic behaviour of solutions to a linear functional equation",
journal = "Opuscula Math.",
year = "2012",
volume = "32",
number = "3",
pages = "559--577",
doi = "http://dx.doi.org/10.7494/OpMath.2012.32.3.559",
url = "http://dx.doi.org/10.7494/OpMath.2012.32.3.559",
abstract = "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.",
keywords = "linear functional equations and inequalities, solutions with a constant sign, asymptotic behaviour of solutions",
issn = "1232-9274"
}