Nonexistence of Nontrivial Weak Solutions of Some Nonlinear Inequalities with Gradient Nonlinearity
- 作者: Admasu V.E.1, Galakhov E.I.1, Salieva O.A.2
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隶属关系:
- Peoples’ Friendship University of Russia (RUDN University)
- Moscow State Technological University “Stankin”
- 期: 卷 67, 编号 1 (2021): Partial Differential Equations
- 页面: 1-13
- 栏目: Articles
- URL: https://journals.rcsi.science/2413-3639/article/view/327657
- DOI: https://doi.org/10.22363/2413-3639-2021-67-1-1-13
- ID: 327657
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详细
In this article, we modify the results obtained by Mitidieri and Pohozaev on sufficient conditions for the absence of nontrivial weak solutions to nonlinear inequalities and systems with integer powers of|the Laplace operator and with a nonlinear term of the form a(x)|∇(Δmu)|q+ b(x)|∇u|s. We obtainoptimal a priori estimates by applying the nonlinear capacity method with an appropriate choice of testfunctions. As a result, we prove the absence of nontrivial weak solutions to nonlinear inequalities and systems by contradiction.
作者简介
V. Admasu
Peoples’ Friendship University of Russia (RUDN University)
编辑信件的主要联系方式.
Email: galakhov@rambler.ru
Moscow, Russia
E. Galakhov
Peoples’ Friendship University of Russia (RUDN University)
Email: galakhov@rambler.ru
Moscow, Russia
O. Salieva
Moscow State Technological University “Stankin”
Email: olga.a.salieva@gmail.com
Moscow, Russia
参考
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