Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity
The paper is devoted to the study of the solvability of a nonlinear Volterra–Stieltjes integral equation in the class of real functions defined, bounded and continuous on the real half-axis $\mathbb{R}_+$ and having finite limits at infinity. The considered class of integral equations contains, as s...
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| Format: | Article |
| Language: | English |
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University of Szeged
2017-06-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5502 |
| _version_ | 1827951231420596224 |
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| author | Jozef Banas Agnieszka Dubiel |
| author_facet | Jozef Banas Agnieszka Dubiel |
| author_sort | Jozef Banas |
| collection | DOAJ |
| description | The paper is devoted to the study of the solvability of a nonlinear Volterra–Stieltjes integral equation in the class of real functions defined, bounded and continuous on the real half-axis $\mathbb{R}_+$ and having finite limits at infinity. The considered class of integral equations contains, as special cases, a few types of nonlinear integral equations. In particular, that class contains the Volterra–Hammerstein integral equation and the Volterra–Wiener–Hopf integral equation, among others. The basic tools applied in our study is the classical Schauder fixed point principle and a suitable criterion for relative compactness in the Banach space of real functions defined, bounded and continuous on $\mathbb{R}_+$. Moreover, we will utilize some facts and results from the theory of functions of bounded variation. |
| first_indexed | 2024-04-09T13:38:33Z |
| format | Article |
| id | doaj.art-980e446746934dc9aa1cd2721b57789d |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:38:33Z |
| publishDate | 2017-06-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-980e446746934dc9aa1cd2721b57789d2023-05-09T07:53:07ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752017-06-0120175311710.14232/ejqtde.2017.1.535502Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinityJozef Banas0Agnieszka Dubiel1Rzeszów University of Technology, Rzeszów, PolandRzeszów University of Technology, Rzeszów, PolandThe paper is devoted to the study of the solvability of a nonlinear Volterra–Stieltjes integral equation in the class of real functions defined, bounded and continuous on the real half-axis $\mathbb{R}_+$ and having finite limits at infinity. The considered class of integral equations contains, as special cases, a few types of nonlinear integral equations. In particular, that class contains the Volterra–Hammerstein integral equation and the Volterra–Wiener–Hopf integral equation, among others. The basic tools applied in our study is the classical Schauder fixed point principle and a suitable criterion for relative compactness in the Banach space of real functions defined, bounded and continuous on $\mathbb{R}_+$. Moreover, we will utilize some facts and results from the theory of functions of bounded variation.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5502space of continuous and bounded functionsvariation of functionfunction of bounded variationriemann–stieltjes integralcriterion of relative compactnessintegral equationschauder fixed point principle |
| spellingShingle | Jozef Banas Agnieszka Dubiel Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity Electronic Journal of Qualitative Theory of Differential Equations space of continuous and bounded functions variation of function function of bounded variation riemann–stieltjes integral criterion of relative compactness integral equation schauder fixed point principle |
| title | Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity |
| title_full | Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity |
| title_fullStr | Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity |
| title_full_unstemmed | Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity |
| title_short | Solvability of a Volterra–Stieltjes integral equation in the class of functions having limits at infinity |
| title_sort | solvability of a volterra stieltjes integral equation in the class of functions having limits at infinity |
| topic | space of continuous and bounded functions variation of function function of bounded variation riemann–stieltjes integral criterion of relative compactness integral equation schauder fixed point principle |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=5502 |
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