Multiple positive solutions of some nonlinear heat flow problems

J. R. L. Webb

doi:10.3934/proc.2005.2005.895

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2005, Volume 2005: 895-903. Doi: 10.3934/proc.2005.2005.895 open access

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Multiple positive solutions of some nonlinear heat flow problems

J. R. L. Webb^1,

1.
Department of Mathematics, University of Glasgow, Glasgow G12 8QW

Received: June 30, 2004

Revised: February 28, 2005

Published: August 2005

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Abstract

We give improved results on the existence of multiple positive solutions for a nonlinear heat flow problem with nonlocal boundary conditions. These results utilise some recent work in \cite{jwkleig} and involve the principal eigenvalue of a related linear problem. We also investigate constants that have previously been employed in the study of positive solutions. We obtain the optimal values of these constants but show that using eigenvalues, when possible, gives better results.

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Mathematics Subject Classification: Primary: 34B10, 34B18; Secondary: 47H11, 47H30.

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