Nonexistence of solutions of semilinear inequalities in cone-like domains (Q1772530)

Nonexistence of global solutions to semilinear elliptic and `higher-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, a result of \textit{S. Ohta} and \textit{A. Kaneko} [J. Fac. Sci., Univ. Tokyo, Sect. I A 40, No. 3, 635--650 (1993; Zbl 0799.35126 )] concerning Fujita's exponents on product domains. Our approach is based on the test-function method [cf. \textit{S. Pohozaev} and \textit{L. Véron}, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 29, No. 2, 393--420 (2000; Zbl 0965.35197)]