On uniqueness of positive entire solutions and other properties of linear parabolic equations

Peter Poláčik

doi:10.3934/dcds.2005.12.13

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2005, Volume 12, Issue 1: 13-26. Doi: 10.3934/dcds.2005.12.13

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On uniqueness of positive entire solutions and other properties of linear parabolic equations

Peter Poláčik^1,

1.
School of Mathematics, University of Minnesota, Minneapolis, MN 55455

Received: March 2003

Revised: October 2004

Published: April 2005

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Abstract

We give a simple proof of the uniqueness, up to scalar multiples, of positive entire solutions of linear nonautonomous parabolic equations. The proof is based on a new result on exponential growth of certain expressions involving solutions of the adjoint equation. We also discuss the relation of this result to the exponential separation theorem.

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Mathematics Subject Classification: 35K20, 35B05, 35B40.

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