# American Institute of Mathematical Sciences

January  2005, 12(1): 13-26. doi: 10.3934/dcds.2005.12.13

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

 1 School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States

Received  March 2003 Revised  October 2004 Published  December 2004

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.
Citation: Peter Poláčik. On uniqueness of positive entire solutions and other properties of linear parabolic equations. Discrete & Continuous Dynamical Systems - A, 2005, 12 (1) : 13-26. doi: 10.3934/dcds.2005.12.13
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