Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

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

Pages: 13 - 26, Volume 12, Issue 1, January 2005      doi:10.3934/dcds.2005.12.13

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Peter Poláčik - School of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States (email)

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.

Keywords:  Second order parabolic equations, entire solutions, uniqueness, exponential separation.
Mathematics Subject Classification:  35K20, 35B05, 35B40.

Received: March 2003;      Revised: October 2004;      Available Online: December 2004.