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

Feliz Minhós and Robert de Sousa
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Feliz Minhós: 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
Robert de Sousa: 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

Mathematics, 2020, vol. 8, issue 1, 1-9

Abstract: 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.

Keywords: coupled systems; Hammerstein integral equations; real line; L ? -Carathéodory functions; Schauder’s fixed point Theorem; infinite beams (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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