Geodesic
On nonexistence of nonnegative solutions for some quasilinear elliptic inequalities in a bounded domain
Eurasian mathematical journal, Tome 8 (2017) no. 4, pp. 74-83.

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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. 
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O. A. Salieva. On nonexistence of nonnegative solutions for some quasilinear elliptic inequalities in a bounded domain. Eurasian mathematical journal, Tome 8 (2017) no. 4, pp. 74-83. http://geodesic.mathdoc.fr/item/EMJ_2017_8_4_a8/

[1] H. Brezis, X. Cabré, “Some simple nonlinear PDE's without solutions”, Boll. Un. Mat. Ital. B: Artic. Ric. Mat., ser. 8, 1 (1998), 223–262 | MR

[2] A. Farina, J. Serrin, “Entire solutions of completely coercive quasilinear elliptic equations”, J. Diff. Eq., 250 (2011), 4367–4408 | DOI | MR

[3] A. Farina, J. Serrin, “Entire solutions of completely coercive quasilinear elliptic equations II”, J. Diff. Eq., 250 (2011), 4409–4436 | DOI | MR

[4] R. Filippucci, P. Pucci, M. Rigoli, “Nonlinear weighted p-Laplacian elliptic inequalities with gradient terms”, Commun. Contemp. Math., 12 (2010), 501–535 | DOI | MR

[5] E. Galakhov, O. Salieva, “On blow-up of solutions to differential inequalities with singularities on unbounded sets”, JMAA, 408 (2013), 102–113 | MR

[6] E. Galakhov, O. Salieva, “Blow-up of solutions of some nonlinear inequalities with singularities on unbounded sets”, Math. Notes, 98:4 (2015), 222–229 | DOI | MR

[7] X. Li, F. Li, “Nonexistence of solutions for singular quasilinear differential inequalities with a gradient nonlinearity”, Nonl. Anal. TMA, 75 (2012), 2812–2822 | DOI | MR

[8] E. Mitidieri, S. Pohozaev, “A priori estimates and nonexistence of solutions of nonlinear partial differential equations and inequalitites”, Proc. Stekl. Inst., 234, 2001, 3–383 | MR

[9] S. Pohozaev, “Essentially nonlinear capacities induced by differential operators”, Dokl. RAN, 357 (1997), 592–594 | MR