On absence of nonnegative monotone solutions for some coercive inequalities in a~half-space
Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 573-585.

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Using the nonlinear capacity method, we investigate the problem of absence of nonnegative monotone solutions for a quasilinear elliptic inequality of type $\Delta_pu\ge u^q$ in a half-space in terms of parameters $p$ and $q$.
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E. I. Galakhov; O. A. Salieva. On absence of nonnegative monotone solutions for some coercive inequalities in a~half-space. Contemporary Mathematics. Fundamental Directions, Differential and functional differential equations, Tome 63 (2017) no. 4, pp. 573-585. http://geodesic.mathdoc.fr/item/CMFD_2017_63_4_a2/

[1] E. Mitidieri, S. I. Pohozaev, “A priori estimates and absence of solutions of nonlinear partial derivatives equations and inequalities”, Tr. MIAN [Proc. Math. Inst. Russ. Acad. Sci.], 234, 2001, 3–383 (in Russian) | MR | Zbl

[2] S. I. Pohozaev, “Essentially nonlinear capacities generated by differential operators”, Dokl. RAN [Rep. Russ. Acad. Sci.], 357 (1997), 592–594 (in Russian) | MR | Zbl

[3] Azizieh C., Clément P., “A priori estimates and continuation methods for positive solutions of $p$-Laplace equations”, J. Differ. Equ., 179 (2002), 213–245 | DOI | MR | Zbl

[4] Berestycki H., Capuzzo Dolcetta I., Nirenberg L., “Superlinear indefinite elliptic problems and nonlinear Liouville theorems”, Topol. Methods Nonlinear Anal., 4 (1994), 59–78 | DOI | MR | Zbl

[5] Bidaut-Véron M. F., Pohozaev S. I., “Nonexistence results and estimates for some nonlinear elliptic problems”, J. Anal. Math., 84 (2001), 1–49 | DOI | MR | Zbl

[6] Birindelli I., Mitidieri E., “Liouville theorems for elliptic inequalities and applications”, Proc. Roy. Soc. Edinburgh A, 128 (1998), 1217–1247 | DOI | MR | Zbl

[7] Dancer E. N., Du Y., Efendiev M., “Quasilinear elliptic equations on half- and quarter-spaces”, Adv. Nonlinear Stud., 13 (2013), 115–136 | MR | Zbl

[8] Farina A., Montoro L., Sciunzi B., “Monotonicity and one-dimensional symmetry for solutions of $-\Delta_pu=f(u)$ in half-spaces”, Calc. Var. Part. Differ. Equ., 43 (2012), 123–145 | DOI | MR | Zbl

[9] Farina A., Montoro L., Sciunzi B., “Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces”, Math. Ann., 357 (2013), 855–893 | DOI | MR | Zbl

[10] Farina A., Montoro L., Sciunzi B., Monotonicity in half-spaces of positive solutions to $-\Delta_pu=f(u)$ in the case $p>2$, 2015, arXiv: 1509.03897v1[math.AP]

[11] Filippucci R., “A Liouville result on a half space”, Recent Trends in Nonlinear Partial Differential Equations, Proc. Workshop (Perugia, 2012), v. II, Stationary Problems, Am. Math. Soc., Providence, 2013, 237–252 | DOI | MR | Zbl

[12] Galakhov E., Salieva O., “On blow-up of solutions to differential inequalities with singularities on unbounded sets”, J. Math. Anal. Appl., 408 (2013), 102–113 | DOI | MR | Zbl

[13] Galakhov E., Salieva O., “Blow-up for nonlinear inequalities with singularities on unbounded sets”, Current Trends in Analysis and its Applications, Proc. IXth ISAAC Congress (Krakow, Poland, 2014), Birkhäuser, Basel, 2015, 299-305 | DOI | MR | Zbl

[14] Porretta A., Veron L., “Separable solutions of quasilinear Lane–Emden equations”, J. Eur. Math. Soc., 15 (2013), 755–774 | DOI | MR | Zbl

[15] Zou H., “A priori estimates and existence for quasi-linear elliptic equations”, Calc. Var. Part. Differ. Equ., 33 (2008), 417–437 | DOI | MR | Zbl