On Absence of Nonnegative Monotone Solutions for Some Coercive Inequalities in a Half-Space
- Authors: Galakhov EI1, Salieva OA2
-
Affiliations:
- RUDN University
- Moscow State Technological University “Stankin”
- Issue: Vol 63, No 4 (2017): Differential and Functional Differential Equations
- Pages: 573-585
- Section: New Results
- URL: https://journals.rudn.ru/CMFD/article/view/22401
- DOI: https://doi.org/10.22363/2413-3639-2017-63-4-573-585
Cite item
Full Text
Abstract
Using the nonlinear capacity method, we investigate the problem of absence of nonnegative monotone solutions for a quasilinear elliptic inequality of type Δpu≥uq in a half-space in terms of parameters p and q.
About the authors
E I Galakhov
RUDN University
Email: galakhov@rambler.ru
6 Miklukho-Maklaya st., 117198 Moscow, Russia
O A Salieva
Moscow State Technological University “Stankin”
Email: olga.a.salieva@gmail.com
1 Vadkovskii per., 127055 Moscow, Russia
References
- Митидиери Э., Похожаев С. И. Априорные оценки и отсутствие решений нелинейных уравнений и неравенств в частных производных// Тр. МИАН. - 2001. - 234. - С. 3-383.
- Похожаев С. И. Существенно нелинейные емкости, порожденные дифференциальными операторами// Докл. РАН. - 1997. - 357. - С. 592-594.
- Azizieh C., Cle´ment P. A priori estimates and continuation methods for positive solutions of p-Laplace equations// J. Differ. Equ. - 2002. - 179. - С. 213-245.
- Berestycki H., Capuzzo Dolcetta I., Nirenberg L. Superlinear indefinite elliptic problems and nonlinear Liouville theorems// Topol. Methods Nonlinear Anal. - 1994. - 4. - С. 59-78.
- Bidaut-Ve´ron M. F., Pohozaev S. I. Nonexistence results and estimates for some nonlinear elliptic problems// J. Anal. Math. - 2001. - 84.- С. 1-49.
- Birindelli I., Mitidieri E. Liouville theorems for elliptic inequalities and applications// Proc. Roy. Soc. Edinburgh. - 1998. - 128A. - С. 1217-1247.
- Dancer E. N., Du Y., Efendiev M. Quasilinear elliptic equations on halfand quarter-spaces// Adv. Nonlinear Stud. - 2013. - 13. - С. 115-136.
- Farina A., Montoro L., Sciunzi B. Monotonicity and one-dimensional symmetry for solutions of -Δpu = f (u) in half-spaces// Calc. Var. Part. Differ. Equ. - 2012. - 43. - С. 123-145.
- Farina A., Montoro L., Sciunzi B. Monotonicity of solutions of quasilinear degenerate elliptic equation in half-spaces// Math. Ann. - 2013. - 357. - С. 855-893.
- Farina A., Montoro L., Sciunzi B. Monotonicity in half-spaces of positive solutions to -Δpu = f (u) in the case p > 2// arXiv:1509.03897v1 [math.AP]. - 2015.
- Filippucci R. A Liouville result on a half space// В сб.: «Recent Trends in Nonlinear Partial Differential Equations, II: Stationary Problems»: Proc. Workshop, Perugia, 2012. - Providence: Am. Math. Soc., 2013. - С. 237-252.
- Galakhov E., Salieva O. On blow-up of solutions to differential inequalities with singularities on unbounded sets// J. Math. Anal. Appl. - 2013. - 408. - С. 102-113.
- 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. - Basel: Birkha¨user, 2015. - С. 299-305.
- Porretta A., Veron L. Separable solutions of quasilinear Lane-Emden equations// J. Eur. Math. Soc. - 2013. - 15. - С. 755-774.
- Zou H. A priori estimates and existence for quasi-linear elliptic equations// Calc. Var. Part. Differ. Equ. - 2008. - 33. - С. 417-437.