Absence of positive solutions of some nonlinear inequalities with transformations of the argument in a half-space
- Authors: Galakhov E.I.1, Salieva O.A.2
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Affiliations:
- RUDN University
- Moscow State Technological University “Stankin”
- Issue: Vol 69, No 1 (2023): Differential and Functional Differential Equations
- Pages: 62-72
- Section: Articles
- URL: https://journals.rudn.ru/CMFD/article/view/34594
- DOI: https://doi.org/10.22363/2413-3639-2022-69-1-62-72
- EDN: https://elibrary.ru/ESEMSD
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Abstract
We prove the absence of positive solutions for some semilinear elliptic partial differential inequalities with transformations of the argument in a half-space. The proofs are based on the test functions method.
About the authors
E. I. Galakhov
RUDN University
Author for correspondence.
Email: egalakhov@gmail.com
Moscow, Russia
O. A. Salieva
Moscow State Technological University “Stankin”
Email: olga.a.salieva@gmail.com
Moscow, Russia
References
- Галахов Е. И., Салиева О. А. Отсутствие решений задачи Дирихле для некоторых квазилинейных эллиптических уравнений в полупространстве// Дифф. уравн. - 2016. - 52. - С. 749-760.
- Митидиери Э., Похожаев С. И. Априорные оценки и разрушение решений нелинейных уравнений и неравенств в частных производных// Тр. МИАН. - 2001. - 234. - С. 1-383.
- Похожаев С. И. Существенно нелинейные емкости, порожденные дифференциальными операторами// Докл. РАН. - 1997. - 56. - С. 592-594.
- Bidaut-V´eron M. F., Pohozaev S. 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. Some notes on the method of moving planes// Bull. Aust. Math. Soc. - 1992. - 46. - С. 425-434.
- Dupaigne L., Sirakov B., Souplet Ph. A Liouville-type theorem for the Lane-Emden equation in a halfspace// ArXiv. - 2020. - 2003.11466.
- Farina A., Montoro L., Sciunzi B. Monotonicity in half-spaces of positive solutions to -Δpu = f (u) in the case p > 2// ArXiv. - 2015. - 1509.03897v1.
- 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.
- Galaktionov V., Mitidieri E., Pohozaev S. Blow-up for higher-order parabolic, hyperbolic, dispersion and Schr¨odinger equations. - Boca Raton: CRC Press, 2014.
- Salieva O. On nonexistence of solutions to some nonlinear inequalities with transformed argument// Electron. J. Qual. Theory Differ. Equ. - 2017. - 2017. - С. 3-13.
