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Multiple positive solutions of some nonlinear heat flow problems

Pages: 895 - 903, Issue Special, August 2005

 Abstract        Full Text (187.4K)              

J. R. L. Webb - Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom (email)

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.

Keywords:  Positive solutions, multiplicity, Hammerstein integral equations, thermostat model.
Mathematics Subject Classification:  Primary: 34B10, 34B18; Secondary: 47H11, 47H30.

Received: July 2004;      Revised: March 2005;      Published: September 2005.