We consider, respectively, the Dirichlet problem and the initial-boundary value problem of elliptic and parabolic equations with two power
nonlinearities. We find that these problems are closely related to the so-called quenching problem. We obtain the existence and nonexistence of positive solutions to these problems on bounded and unbounded domains, by using the results of quenching problem and sub-super solution method.
Publié le : 2005-09-14
Classification:
Elliptic equation,
parabolic equation,
quenching problem,
Dirichlet problem,
initial-boundary value problem,
positive solution,
35J25,
35K20
@article{1128703005,
author = {Dai, Qiuyi and Gu, Yonggeng},
title = {Positive solutions of elliptic and parabolic equations with convex-concave nonlinearities},
journal = {Tohoku Math. J. (2)},
volume = {57},
number = {1},
year = {2005},
pages = { 427-445},
language = {en},
url = {http://dml.mathdoc.fr/item/1128703005}
}
Dai, Qiuyi; Gu, Yonggeng. Positive solutions of elliptic and parabolic equations with convex-concave nonlinearities. Tohoku Math. J. (2), Tome 57 (2005) no. 1, pp. 427-445. http://gdmltest.u-ga.fr/item/1128703005/