@article{Castorina2022, 
author = {Daniele Castorina and Giovanni Catino and Carlo Mantegazza},
title = {A triviality result for semilinear parabolic equations},
year = {2022},
journal = {Mathematics in Engineering},
volume = {4},
number = {1},
pages = {1-15},
keywords = {ancient solution, eternal solution, superlinear heat equation},
url = {https://www.sciopen.com/article/10.3934/mine.2022002},
doi = {10.3934/mine.2022002},
abstract = {We show a triviality result for "pointwise" monotone in time, bounded "eternal" solutions of the semilinear heat equation         u          t        =  Δ  u  +      |    u            |              p      on complete Riemannian manifolds of dimension    n  ≥  5 with nonnegative Ricci tensor, when    p is smaller than the critical Sobolev exponent              n      +      2              n      −      2      .}
}