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Open AccessArticle

Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line

by Feliz Minhós 1,2,* and Robert de Sousa 2,3
1
Departamento de Matemática, Escola de Ciências e Tecnologia, Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
2
Centro de Investigação em Matemática e Aplicações (CIMA), Instituto de Investigação e Formação Avançada, Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal
3
Faculdade de Ciências e Tecnologia, Nu´cleo de Matemática e Aplicações (NUMAT), Universidade de Cabo Verde, Campus de Palmarejo, Praia 279, Cabo Verde
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(1), 111; https://doi.org/10.3390/math8010111
Received: 13 November 2019 / Revised: 3 January 2020 / Accepted: 4 January 2020 / Published: 10 January 2020
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 R , combined with the equiconvergence at ± 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. View Full-Text
Keywords: coupled systems; Hammerstein integral equations; real line; L-Carathéodory functions; Schauder’s fixed point Theorem; infinite beams coupled systems; Hammerstein integral equations; real line; L-Carathéodory functions; Schauder’s fixed point Theorem; infinite beams
MDPI and ACS Style

Minhós, F.; de Sousa, R. Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line. Mathematics 2020, 8, 111.

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