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On the absence of global weak solutions for some differential inequalities of Sobolev type in an exterior domain
Author(s) -
Jleli Mohamed,
Kirane Mokhtar,
Samet Bessem
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5080
Subject(s) - mathematics , sobolev space , domain (mathematical analysis) , type (biology) , mathematical analysis , nonlinear system , sobolev inequality , differential (mechanical device) , inequality , space (punctuation) , pure mathematics , ecology , engineering , biology , aerospace engineering , linguistics , philosophy , physics , quantum mechanics
In this paper, using the nonlinear capacity method, we derive sufficient conditions for the nonexistence of global weak solutions for some differential inequalities of Sobolev type posed in an exterior domain of R N , N ≥ 3. The obtained results are extensions of those established by Korpusov and Sveshnikov in the case of the entire space R N .