Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line
In this work, we consider a generalized coupled system of integral equations of Hammerstein-type with, eventually, discontinuous nonlinearities. The main existence tool is Schauder’s fixed point theorem in the space of bounded and continuous functions with bounded and continuous derivative...
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MDPI AG
2020-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/1/111 |
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| author | Feliz Minhós Robert de Sousa |
| author_facet | Feliz Minhós Robert de Sousa |
| author_sort | Feliz Minhós |
| collection | DOAJ |
| description | In this work, we consider a generalized coupled system of integral equations of Hammerstein-type with, eventually, discontinuous nonlinearities. The main existence tool is Schauder’s fixed point theorem in the space of bounded and continuous functions with bounded and continuous derivatives on <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">R</mi> </semantics> </math> </inline-formula>, combined with the equiconvergence at <inline-formula> <math display="inline"> <semantics> <mrow> <mo>±</mo> <mo>∞</mo> </mrow> </semantics> </math> </inline-formula> to recover the compactness of the correspondent operators. To the best of our knowledge, it is the first time where coupled Hammerstein-type integral equations in real line are considered with nonlinearities depending on several derivatives of both variables and, moreover, the derivatives can be of different order on each variable and each equation. On the other hand, we emphasize that the kernel functions can change sign and their derivatives in order to the first variable may be discontinuous. The last section contains an application to a model to study the deflection of a coupled system of infinite beams. |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-11T20:35:21Z |
| publishDate | 2020-01-01 |
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| spelling | doaj.art-2ab46a67d2c94b1b92188013fc1ba7cb2022-12-22T00:51:40ZengMDPI AGMathematics2227-73902020-01-018111110.3390/math8010111math8010111Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real LineFeliz Minhós0Robert de Sousa1Departamento de Matemática, Escola de Ciências e Tecnologia, Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, PortugalCentro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, PortugalIn this work, we consider a generalized coupled system of integral equations of Hammerstein-type with, eventually, discontinuous nonlinearities. The main existence tool is Schauder’s fixed point theorem in the space of bounded and continuous functions with bounded and continuous derivatives on <inline-formula> <math display="inline"> <semantics> <mi mathvariant="double-struck">R</mi> </semantics> </math> </inline-formula>, combined with the equiconvergence at <inline-formula> <math display="inline"> <semantics> <mrow> <mo>±</mo> <mo>∞</mo> </mrow> </semantics> </math> </inline-formula> to recover the compactness of the correspondent operators. To the best of our knowledge, it is the first time where coupled Hammerstein-type integral equations in real line are considered with nonlinearities depending on several derivatives of both variables and, moreover, the derivatives can be of different order on each variable and each equation. On the other hand, we emphasize that the kernel functions can change sign and their derivatives in order to the first variable may be discontinuous. The last section contains an application to a model to study the deflection of a coupled system of infinite beams.https://www.mdpi.com/2227-7390/8/1/111coupled systemshammerstein integral equationsreal line<i>l</i><sup>∞</sup>-carathéodory functionsschauder’s fixed point theoreminfinite beams |
| spellingShingle | Feliz Minhós Robert de Sousa Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line Mathematics coupled systems hammerstein integral equations real line <i>l</i><sup>∞</sup>-carathéodory functions schauder’s fixed point theorem infinite beams |
| title | Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line |
| title_full | Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line |
| title_fullStr | Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line |
| title_full_unstemmed | Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line |
| title_short | Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line |
| title_sort | solvability of coupled systems of generalized hammerstein type integral equations in the real line |
| topic | coupled systems hammerstein integral equations real line <i>l</i><sup>∞</sup>-carathéodory functions schauder’s fixed point theorem infinite beams |
| url | https://www.mdpi.com/2227-7390/8/1/111 |
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