A note on the strong maximum principle and the compact support principle

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Author(s):	Felmer, Patricio ^{[1, 2]} ; Montenegro, Marcelo ^[3] ; Quaas, Alexander ^[4] Total Authors: 3
Affiliation:	^[1] Univ Chile, Dept Ingn Matemat, Santiago - Chile ^[2] Univ Chile, Ctr Modelamiento Matemat, CNRS, UM12807, Santiago - Chile ^[3] Univ Estadual Campinas, Dept Matemat, IMECC, BR-13083970 Campinas, SP - Brazil ^[4] Univ Tecn Feder Santa Maria Casilla, Dept Matemat, Valparaiso - Chile Total Affiliations: 4
Document type:	Journal article
Source:	Journal of Differential Equations; v. 246, n. 1, p. 39-49, JAN 1 2009.
Web of Science Citations:	12
Abstract
In this note we are concerned with the strong maximum principle (SMP) and the compact support principle (CSP) for non-negative solutions to quasilinear elliptic inequalities of the form div (A(vertical bar del i vertical bar del u) + G(vertical bar del u vertical bar) - f(u) <= 0 in Omega, div (A(vertical bar del i vertical bar del u) + G(vertical bar del u vertical bar) - f(u) >= 0 in R(N)\textbackslash{}B(r)(0), respectively. We give new conditions on the data (A, G.f) to obtain (SMP) and (CSP). When these conditions are particularized to the m-Laplacian and pure power nonlinearities we completely classify the data according to the validity of the (CSP) or the (SMP). In doing so we clarify the general situation and we consider a case not covered in the literature. (c) 2008 Elsevier Inc. All rights reserved. (AU)