@article{Cholewa_Dłotko_2003, title={Parabolic equations with critical nonlinearities}, volume={21}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2003.019}, abstractNote={As well known the problem of global continuation of solutions
to semilinear parabolic equations is completely solved when the nonlinear
term is subordinated to an $\alpha$-power of the main linear
operator with $\alpha\in[0,1)$. In this paper we study three
examples of {\it critical problems} in which the mentioned subordination takes place
with $\alpha=1$, i.e. the nonlinearity has the same {\it order of magnitude}
as the linear main part. We use specific techniques of proving global
solvability that fit well the considered examples for which
general abstract methods fail.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Cholewa, Jan W. and Dłotko, Tomasz}, year={2003}, month={Jun.}, pages={311–324} }