Open AccessNonexistence of Nontrivial Weak Solutions of Some Nonlinear Inequalities with Gradient Nonlinearity
Author(s) -
В. Е. Адмасу,
Е. И. Галахов,
Olga Salieva
Publication year - 2021
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2021-67-1-1-13
Subject(s) - nonlinear system , mathematics , integer (computer science) , a priori and a posteriori , term (time) , operator (biology) , monotonic function , laplace transform , inequality , mathematical analysis , pure mathematics , physics , computer science , quantum mechanics , philosophy , biochemistry , chemistry , epistemology , repressor , transcription factor , gene , programming language
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)|(mu)|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.