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Title: Multiplicity of positive solutions for an indefinite superlinear elliptic problem on R^n
Contributor(s): Du, Yihong  (author)
Publication Date: 2004
DOI: 10.1016/j.anihpc.2003.09.002
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Abstract: We consider the elliptic problem -Δu − λu = a(x)u^p, with p >1 and (x) sign-changing. Under suitable conditions on p and a(x), we extend the multiplicity, existence and nonexistence results known to hold for this equation on a bounded domain with standard homogeneous boundary conditions) to the case that the bounded domain is replaced by the entire space R^N. More precisely, we show that there exists ∧>0 such that this equation on R^N has no positive solution for λ>∧, at least two positive solutions for λ ∈ (0,Λ), and at least one positive solution for λ ∊ (−∞, 0] ∪ {Λ}.
Publication Type: Journal Article
Source of Publication: Institut Henri Poincare. Annales (C). Analyse Non Lineaire, 21(5), p. 657-672
Publisher: Elsevier
Place of Publication: France
ISSN: 1873-1430
Field of Research (FOR): 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
Socio-Economic Outcome Codes: 970101 Expanding Knowledge in the Mathematical Sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
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Appears in Collections:Journal Article
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