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Positive Solutions of Nonlinear Equations with Explicit Dependence on the Independent Variable

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Differential and Difference Equations with Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 47))

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Abstract

We discuss positive solutions of integral equations for problems that arise from nonlinear boundary value problems. The boundary conditions can be either of local or nonlocal type. We concentrate on the case where the nonlinear term f(t,u) depends explicitly on t and this dependence is crucial. We give new fixed-point index results using a comparison theorem for a class of linear operators related to the u 0-positive operators of Krasnosel’skiĭ. These are used to establish new results on existence and nonexistence of positive solutions under some conditions which can be sharp.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, University of Glasgow, Glasgow, G12 8QW, UK

    J. R. L. Webb

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  1. J. R. L. Webb
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Correspondence to J. R. L. Webb .

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Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. University of Zürich Institute of Mathematics, Zürich, Switzerland

    Michel Chipot

  3. Masaryk University Dept. Mathematics, Brno, Czech Republic

    Zuzana Dosla

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Webb, J.R.L. (2013). Positive Solutions of Nonlinear Equations with Explicit Dependence on the Independent Variable. In: Pinelas, S., Chipot, M., Dosla, Z. (eds) Differential and Difference Equations with Applications. Springer Proceedings in Mathematics & Statistics, vol 47. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7333-6_11

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