Nonexistence of solutions to semilinear inequalities in conical domains

Nonexistence of global solutions to semilinear elliptic and "heigher- order evolution" inequalities is studied. Two types of domains are considered: product of cones and product of cone-like domains. We find, in particular and with a different method, the result of Ohta & Kaneko [16] concerning Fujita's exponents on product domains. Our approach is based on the test-function method, developed by Mitidieri & Pohozaev [13], Pohozaev & Tesei [18] and Pohozaev Veron [20].