On the asymptotic behaviour of solutions to a linear functional equation
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 \(+\infty\) te...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2012-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3239.pdf |
| _version_ | 1828405344639909888 |
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| author | Dariusz Sokołowski |
| author_facet | Dariusz Sokołowski |
| author_sort | Dariusz Sokołowski |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T10:51:49Z |
| format | Article |
| id | doaj.art-9fc29b286a014b9a8c282bf726cb15e5 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-10T10:51:49Z |
| publishDate | 2012-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-9fc29b286a014b9a8c282bf726cb15e52022-12-22T01:51:59ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742012-01-01323559577http://dx.doi.org/10.7494/OpMath.2012.32.3.5593239On the asymptotic behaviour of solutions to a linear functional equationDariusz Sokołowski0Silesian Universit, Institute of Mathematics, ul. Bankowa 14, 40-007 Katowice, PolandWe 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.http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3239.pdflinear functional equations and inequalitiessolutions with a constant signasymptotic behaviour of solutions |
| spellingShingle | Dariusz Sokołowski On the asymptotic behaviour of solutions to a linear functional equation Opuscula Mathematica linear functional equations and inequalities solutions with a constant sign asymptotic behaviour of solutions |
| title | On the asymptotic behaviour of solutions to a linear functional equation |
| title_full | On the asymptotic behaviour of solutions to a linear functional equation |
| title_fullStr | On the asymptotic behaviour of solutions to a linear functional equation |
| title_full_unstemmed | On the asymptotic behaviour of solutions to a linear functional equation |
| title_short | On the asymptotic behaviour of solutions to a linear functional equation |
| title_sort | on the asymptotic behaviour of solutions to a linear functional equation |
| topic | linear functional equations and inequalities solutions with a constant sign asymptotic behaviour of solutions |
| url | http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3239.pdf |
| work_keys_str_mv | AT dariuszsokołowski ontheasymptoticbehaviourofsolutionstoalinearfunctionalequation |