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Comparison results for nonlinear elliptic equations with lower–order terms
Author(s) -
Ferone Vincenzo,
Messano Basilio
Publication year - 2003
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.200310036
Subject(s) - mathematics , nonlinear system , elliptic operator , principal part , homogeneous , operator (biology) , order (exchange) , term (time) , dirichlet problem , class (philosophy) , mathematical analysis , sign (mathematics) , omega , pure mathematics , semi elliptic operator , dirichlet distribution , elliptic curve , combinatorics , boundary value problem , differential operator , physics , biochemistry , chemistry , repressor , quantum mechanics , artificial intelligence , computer science , transcription factor , gene , finance , economics
We consider a solution u of the homogeneous Dirichlet problem for a class of nonlinear elliptic equations in the form A ( u ) + g ( x , u ) = f , where the principal term is a Leray–Lions operator defined on $ W ^{1, p} _{0} (\Omega) $ and g ( x , u ) is a term having the same sign as u and satisfying suitable growth assumptions. We prove that the rearrangement of u can be estimated by the solution of a problem whose data are radially symmetric.