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Neural Computing and Applications
Published in: Neural Computing and Applications 16/2020

24-01-2020 | Original Article

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

Authors: Feliz Minhós, Hugo Carrasco

Published in: Neural Computing and Applications | Issue 16/2020

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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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Metadata
Title
Lidstone-type problems on the whole real line and homoclinic solutions applied to infinite beams
Authors
Feliz Minhós
Hugo Carrasco
Publication date
24-01-2020
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 16/2020
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-020-04732-x

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