Absence of solutions of differential inequalities and systems of hyperbolic type in conic domains

©, 2002 Russian Academy of Sciences, (DoM) and London Mathematical Society, Turpion Ltd
, , Citation G G Laptev 2002 Izv. Math. 66 1147 DOI 10.1070/IM2002v066n06ABEH000410

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1 Tula State University, Tula, Russian Federation

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1064-5632/66/6/1147

Abstract

We establish conditions sufficient for the absence of global solutions of semilinear hyperbolic inequalities and systems in conic domains of the Euclidean space .

We consider a model problem in a cone : that given by the inequality

The proof is based on the test-function method developed by Veron, Mitidieri, Pokhozhaev, and Tesei.

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