Electron. J. Diff. Eqns. Vol. 1995(1995), No. 14, pp. 1-13.

Picones's Identity and the Moving Plane Procedure

W. Allegretto & D. Siegel

Abstract:
Positive solutions of a class of nonlinear elliptic partial differential equations are shown to be symmetric by means of the moving plane argument coupled with Spectral Theory results and Picone's Identity. The method adapts easily to situations where the moving plane procedure gives rise to variational problems with positive eigenfunctions.

Submitted April 15, 1995. Published October 6 ,1995.
Math Subject Classification: 35B05, 35J60.
Key Words: symmetry, positive solutions, nonlinear elliptic, moving plane, Spectral Theory, Picone's Identity.

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Walter Allegretto
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
e-mail: retl@retl.math.ualberta.ca

David Siegel
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
e-mail: dsiegel@math.uwaterloo.ca

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