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Existence and location of solutions to fourth-order Lidstone coupled systems with dependence on odd derivatives

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Abstract

This paper addresses the existence and location results for coupled system with two fourth-order differential equations with dependence on all derivatives in nonlinearities and subject to Lidstone-type boundary conditions. To guarantee the existence and location of the solutions, we applied lower and upper solutions technique and degree theory. In this context, we highlight a new type of Nagumo condition to control the growth of the third derivatives and increases the number of applications, as well as a new type of definitions of upper and lower solutions for such coupled systems. Last section contains an application to a coupled system composed by two fourth order equations, which models the estimated bending of simply-supported beam with torsional solitons.

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Authors and Affiliations

  1. Faculdade de Ciências e Tecnologia, Núcleo de Matemática e Aplicações (NUMAT), Universidade de Cabo Verde, Campus de Palmarejo, 279, Praia, Cabo Verde

    Robert de Sousa

  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

    Robert de Sousa & Feliz Minhós

  3. Departamento de Matemática, Escola de Ciências e Tecnologia, 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

    Feliz Minhós

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  1. Robert de Sousa
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  2. Feliz Minhós
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Correspondence to Robert de Sousa.

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Communicated by Julio Rossi.

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de Sousa, R., Minhós, F. Existence and location of solutions to fourth-order Lidstone coupled systems with dependence on odd derivatives. Adv. Oper. Theory 6, 10 (2021). https://doi.org/10.1007/s43036-020-00105-2

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  • DOI: https://doi.org/10.1007/s43036-020-00105-2

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