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Three-point boundary value problems in Banach spaces

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Abstract

Using degree for \(\alpha \)-condensing maps, we obtain the existence of at least one solution for nonlinear boundary value problems

$$\begin{aligned} \left\{ \begin{array}{lll} (\varphi (u' ))' = f(t,u,u') &{} &{} \\ u(0)=u(1)=u'(0), &{} &{} \quad \quad \end{array}\right. \end{aligned}$$

where \(\varphi : X\rightarrow X \) is a linear homeomorphism, \(f:\left[ 0, 1\right] \times X \times X \rightarrow X \) is a continuous function and X is a real Banach space.

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Acknowledgements

This research was supported by CAPES and CNPq/Brazil.

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  1. Department of Mathematics, IME-USP, Cidade Universitária, São Paulo, SP, CEP 05508-090, Brazil

    Dionicio Pastor Dallos Santos

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  1. Dionicio Pastor Dallos Santos
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Correspondence to Dionicio Pastor Dallos Santos.

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Santos, D.P.D. Three-point boundary value problems in Banach spaces. Bol. Soc. Mat. Mex. 25, 351–362 (2019). https://doi.org/10.1007/s40590-018-0200-3

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  • DOI: https://doi.org/10.1007/s40590-018-0200-3

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