Abstract
This paper presents sufficient conditions for the solvability of the third order three point boundary value problem
The arguments apply Green’s function associated to the linear problem and the Guo–Krasnosel’skiĭ theorem of compression-expansion cones. The dependence on the first derivatives is overcome by the construction of an adequate cone and suitable conditions of superlinearity/sublinearity near 0 and \(+\infty \). Last section contains an example to illustrate the applicability of the theorem.
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First author was supported by National Founds through FCT-Fundação para a Ciência e a Tecnologia, project SFRH/BSAB/114246/2016.
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Minhós, F., de Sousa, R. On the Solvability of Third-Order Three Point Systems of Differential Equations with Dependence on the First Derivative. Bull Braz Math Soc, New Series 48, 485–503 (2017). https://doi.org/10.1007/s00574-016-0025-5
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DOI: https://doi.org/10.1007/s00574-016-0025-5