TY  - JOUR
ID  - Sokołowski2012
LB  - Sokołowski2012
AU  - Sokołowski, Dariusz
TI  - On the asymptotic behaviour of solutions to a linear functional equation
ST  - On the asymptotic behaviour of solutions to a linear functional equation
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2012
VL  - 32
IS  - 3
SP  - 559
EP  - 577
DO  - http://dx.doi.org/10.7494/OpMath.2012.32.3.559
UR  - http://dx.doi.org/10.7494/OpMath.2012.32.3.559
AB  - 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.
KW  - linear functional equations and inequalities
KW  - solutions with a constant sign
KW  - asymptotic behaviour of solutions
SN  - 1232-9274
ER  -