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Existence and nonexistence results for reaction-diffusion equations in product of cones

Abdallah HamidiGennady Laptev — 2003

Open Mathematics

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.

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