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Differential Equations with Involutions pp 125–151Cite as

A Cone Approximation to a Problem with Reflection

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Abstract

In this chapter we continue this study and we prove new results regarding the existence of nontrivial solutions of Hammerstein integral equations with reflections of the form

$$\begin{aligned} u(t)=\int _{-T}^{T} k(t,s)g(s)f(s,u(s),u(-s))\mathrm {d}s,\quad t\in [-T,T], \end{aligned}$$

where the kernel k is allowed to be not of constant sign.

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Authors and Affiliations

  1. Departamento de Análise Matemática, Universidade de Santiago de Compostela, Santiago de Compostela, Spain

    Alberto Cabada & F. Adrián F. Tojo

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  1. Alberto Cabada
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  2. F. Adrián F. Tojo
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Correspondence to Alberto Cabada .

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Cabada, A., Tojo, F.A.F. (2015). A Cone Approximation to a Problem with Reflection. In: Differential Equations with Involutions. Atlantis Briefs in Differential Equations. Atlantis Press, Paris. https://doi.org/10.2991/978-94-6239-121-5_6

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