Abstract
We consider a class of semilinear heat equations on ℝ, including in particular the Fujita equation (Equation presented) where p > 1. We first give a simple proof and an extension of a Liouville theorem concerning entire solutions with finite zero number. Then we show that there is an infinite-dimensional set of entire solutions with infinite zero number.
Original language | English (US) |
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Pages (from-to) | 2997-3008 |
Number of pages | 12 |
Journal | Proceedings of the American Mathematical Society |
Volume | 148 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2020 |
Bibliographical note
Publisher Copyright:© 2020 American Mathematical Society.
Keywords
- Entire solutions
- Liouville theorems
- Semilinear parabolic equations
- Zero number