Geodesic
Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains
Izvestiya. Mathematics , Tome 66 (2002) no. 6, pp. 1147-1170.

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We establish conditions sufficient for the absence of global solutions of semilinear hyperbolic inequalities and systems in conic domains of the Euclidean space RN. We consider a model problem in a cone K: that given by the inequality $$ \dfrac{\partial^2u}{\partial t^2}-\Delta u\geqslant |u|^q, \qquad (x,t)\in K\times(0,\infty), $$ The proof is based on the test-function method developed by Veron, Mitidieri, Pokhozhaev, and Tesei. 
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G. G. Laptev. Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains. Izvestiya. Mathematics , Tome 66 (2002) no. 6, pp. 1147-1170. https://geodesic-test.mathdoc.fr/item/IM2_2002_66_6_a3/

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