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Multiple positive solutions of some nonlinear heat flow problems

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


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