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

Author

Listed:
  • 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
    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)

  • 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
    Faculdade de Ciências e Tecnologia, Nu´cleo de Matemática e Aplicações (NUMAT), Universidade de Cabo Verde, Campus de Palmarejo, Praia 279, Cabo Verde)

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.

Suggested Citation

  • Feliz Minhós & Robert de Sousa, 2020. "Solvability of Coupled Systems of Generalized Hammerstein-Type Integral Equations in the Real Line," Mathematics, MDPI, vol. 8(1), pages 1-9, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:111-:d:307462
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