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Loss of positivity in a nonlinear scalar heat equation

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Nonlinear Differential Equations and Applications NoDEA Aims and scope Submit manuscript

Abstract.

Using the theory of fixed point index, we discuss the existence of nontrivial (multiple) solutions of a nonlinear scalar heat equation with nonlocal boundary conditions depending on a positive parameter. Solutions lose positivity as the parameter decreases. For a certain parameter range, not all solutions can be positive but there are positive solutions for certain types of nonlinearity. We also prove a uniqueness result.

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Authors and Affiliations

  1. Dipartimento di Mathematica, Università della Calabria, 87036, Arcavacata di Rende, Cosenza, Italy

    Gennaro Infante

  2. Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, United Kingdom

    J. R. L. Webb

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  1. Gennaro Infante
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  2. J. R. L. Webb
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Correspondence to Gennaro Infante.

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Infante, G., Webb, J.R.L. Loss of positivity in a nonlinear scalar heat equation. Nonlinear differ. equ. appl. 13, 249–261 (2006). https://doi.org/10.1007/s00030-005-0039-y

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  • DOI: https://doi.org/10.1007/s00030-005-0039-y

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