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On nonexistence of nonnegative solutions for some quasilinear elliptic inequalities in a bounded domain

O. A. Salieva

Department of Applied Mathematics, Moscow State Technological University "Stankin", 1 Vadkovsky pereulok, 127005 Moscow, Russia

Abstract: Using the test function method, we study sufficient conditions of nonexistence of nonnegative solutions for a quasilinear elliptic inequality of the form $-\mathrm{div}(u^r|Du|^{p-2}Du)\geqslant a(x)u^q|Du|^s$ in a bounded domain and its generalizations.

Keywords and phrases: quasilinear elliptic inequalities; nonexistence of solutions.

MSC: 35A01, 35J87, 35J92

Received: 30.12.2016

Language: English

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