Existence and Nonexistence Results for Reaction-Diffusion Equations in Product of Cones

Abdallah El Hamidi and Gennady G. Laptev

Université de la Rochelle

Avenue Michel Crépeau

17042 La Rochelle Cedex 1

France

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, Véron. The existence result is established using the method of supersolutions.