TY - JOUR
AU - Cholewa, Jan W.
AU - DÅ‚otko, Tomasz
PY - 2003/06/01
Y2 - 2021/12/03
TI - Parabolic equations with critical nonlinearities
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 21
IS - 2
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2003.019
SP - 311 - 324
AB - As well known the problem of global continuation of solutionsto semilinear parabolic equations is completely solved when the nonlinearterm is subordinated to an $\alpha$-power of the main linearoperator with $\alpha\in[0,1)$. In this paper we study threeexamples of {\it critical problems} in which the mentioned subordination takes placewith $\alpha=1$, i.e. the nonlinearity has the same {\it order of magnitude}as the linear main part. We use specific techniques of proving globalsolvability that fit well the considered examples for whichgeneral abstract methods fail.
ER -