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Lidstone-type problems on the whole real line and homoclinic solutions applied to infinite beams

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Abstract

This work provides sufficient conditions for the existence of solutions to fourth-order nonlinear ordinary differential equations with Lidstone-type boundary conditions on the real line. Using Green’s functions, we formulate a modified integral equation and correspondent integral operators, in which fixed points are the solutions of the initial problem. Moreover, it is proved that every solution of the Lidstone problem on the whole real line is an homoclinic solution.

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Authors and Affiliations

  1. Centro de Investigação em Matemática e Aplicações (CIMA), 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

    Feliz Minhós

  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

    Hugo Carrasco

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  1. Feliz Minhós
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  2. Hugo Carrasco
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Correspondence to Feliz Minhós.

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Minhós, F., Carrasco, H. Lidstone-type problems on the whole real line and homoclinic solutions applied to infinite beams. Neural Comput & Applic 32, 12873–12879 (2020). https://doi.org/10.1007/s00521-020-04732-x

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