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On positive solutions of minimal growth for singular p-Laplacian with potential term
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2008 (English)In: Advanced Nonlinear Studies, ISSN 1536-1365, Vol. 8, no 2, 213-234 p.Article in journal (Refereed) Published
Abstract [en]

Let Omega be a domain in R-d, d >= 2, and 1 < p < infinity. Fix V is an element of L-loc(infinity)(Omega) Consider the functional Q and its Gdteaux derivative Q(') given by Q(u):=1/p integral(Omega)(|del u|(p)+V|u|(p))dx, Q'(u):=-del. (|del u|(p-2)del u) + V|u|(p-2)u. It is assumed that Q >= 0 on C-0(infinity)(Omega). In a previous paper [221 we discussed relations between the absence of weak coercivity of the functional Q on C-0(infinity) (Omega) and the existence of a generalized ground state. In the present paper we study further relationships between functional-analytic properties of the functional Q and properties of positive solutions of the equation Q'(u) = 0.

Place, publisher, year, edition, pages
2008. Vol. 8, no 2, 213-234 p.
Keyword [en]
quasilinear elliptic operator, p-Laplacian, ground state, positive solutions, comparison principle, minimal growth
National Category
URN: urn:nbn:se:uu:diva-110414ISI: 000255261700001OAI: oai:DiVA.org:uu-110414DiVA: diva2:277229
Available from: 2009-11-16 Created: 2009-11-16 Last updated: 2010-01-13Bibliographically approved

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