American Institute of Mathematical Sciences

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2005, 2005(Special): 895-903. doi: 10.3934/proc.2005.2005.895

Multiple positive solutions of some nonlinear heat flow problems

J. R. L. Webb 1,

1. 

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

Received  July 2004 Revised  March 2005 Published  September 2005

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.
Keywords: thermostat model., multiplicity, Positive solutions, Hammerstein integral equations.
Mathematics Subject Classification: Primary: 34B10, 34B18; Secondary: 47H11, 47H3.
Citation: J. R. L. Webb. Multiple positive solutions of some nonlinear heat flow problems. Conference Publications, 2005, 2005 (Special) : 895-903. doi: 10.3934/proc.2005.2005.895
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