Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.
@article{bwmeta1.element.doi-10_2478_BF02475664,
author = {Abdallah Hamidi and Gennady Laptev},
title = {Existence and nonexistence results for reaction-diffusion equations in product of cones},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {61-78},
zbl = {1019.35045},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475664}
}
Abdallah Hamidi; Gennady Laptev. Existence and nonexistence results for reaction-diffusion equations in product of cones. Open Mathematics, Tome 1 (2003) pp. 61-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475664/
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