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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

Peter Poláčik 1,

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.
Keywords: Second order parabolic equations, exponential separation., entire solutions, uniqueness.
Mathematics Subject Classification: 35K20, 35B05, 35B4.
Citation: Peter Poláčik. On uniqueness of positive entire solutions and other properties of linear parabolic equations. Discrete and Continuous Dynamical Systems, 2005, 12 (1) : 13-26. doi: 10.3934/dcds.2005.12.13
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