On integral operators and nonlinear integral equations in the spaces of functions of bounded variation

Dariusz Bugajewski , Jacek Gulgowski , Piotr Kasprzak

Abstract

In this paper we introduce new conditions on a kernel of a linear Fredholm integral operator which turn out to be sufficient and necessary for that operator to map the space of functions of bounded variation in the sense of Jordan into itself. Furthermore, we apply those conditions to deal with the problem of the existence of solutions to nonlinear Hammerstein equations in that space. To achieve our goals we will use a topological degree approach as well as a fixed point approach.
Author Dariusz Bugajewski
Dariusz Bugajewski,,
-
, Jacek Gulgowski IM
Jacek Gulgowski,,
- Institute of Mathematics
, Piotr Kasprzak
Piotr Kasprzak,,
-
Journal seriesJournal of Mathematical Analysis and Applications, ISSN 0022-247X
Issue year2016
Vol444
No1
Pages230-250
Publication size in sheets1
Keywords in Englishlinear integral operator of a Fredholm-type, Leray-Schauder degree, nonlinear Hammerstein integral equation, variation in the sense of Jordan, weakly singular kernel, φ- and Λ-variation
DOIDOI:10.1016/j.jmaa.2016.06.014
URL http://dx.doi.org/10.1016/j.jmaa.2016.06.014
Languageen angielski
Score (nominal)40
ScoreMinisterial score = 35.0, 20-12-2017, ArticleFromJournal
Ministerial score (2013-2016) = 40.0, 20-12-2017, ArticleFromJournal
Publication indicators WoS Impact Factor: 2016 = 1.064 (2) - 2016=1.151 (5)
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