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Positive solutions of some quasilinear partial differential inequalities and systems
Author(s) -
Galakhov Evgeny
Publication year - 2006
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310397
Subject(s) - mathematics , gravitational singularity , dimension (graph theory) , nonlinear system , inequality , partial differential equation , boundary (topology) , partial derivative , differential (mechanical device) , mathematical analysis , pure mathematics , thermodynamics , physics , quantum mechanics
Abstract We establish the necessary conditions for existence of positive solutions to elliptic and evolution partial differential inequalities and their systems with singularities at the origin, at the boundary, or on subsets of different dimension. Our basic tool is the nonlinear capacity method due to E. Mitidieri and S. Pohozaev. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)