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Positivity of solutions of elliptic equations with nonlocal terms*

Published online by Cambridge University Press:  14 November 2011

W. Allegretto  and
A. Barabanova
W. Allegretto
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1
A. Barabanova
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1
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Extract

In this paper we study a nonlocal problem for a second-order partial differential equation which depends on a parameter n. We prove the existence of critical values 0 < and 0 > such that for all ≦ɳ≦ and for all non-negative right-hand sides, our problem has nonnegative solutions. We obtain a formula for ɳ0, the maximal possible value of , and find the exact value of ɳ for spherical ɳ. We also study the corresponding eigenvalue problem. At the end of the paper, we consider the application of our results to the nonlinear system describing the distribution of temperature and potential in a microsensor.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 3 , 1996 , pp. 643 - 663
Copyright
Copyright © Royal Society of Edinburgh 1996

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