Nonnegative solutions of elliptic problems with sublinear indefinite nonlinearity

We are concerned with existence, nonexistence and multiplicity of nonnegative solutions for the elliptic problem − Δ u = a ( x ) u q + λ b ( x ) u p in Ω , u = 0 on ∂ Ω , where Ω is a bounded domain in R N , λ ∈ R , 0 < q < 1 < p ⩽ 2 ⁎ − 1 and a, b are bounded functions, with b ( x ) ⩾ 0 an...

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Bibliographic Details
Published inJournal of functional analysis Vol. 261; no. 9; pp. 2569 - 2586
Main Author de Paiva, Francisco Odair
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2011
Subjects
Concave-convex nonlinearity
Critical exponent
Indefinite sublinear nonlinearity
Nonnegative solution
Critical exponent
Nonnegative solution
Concave-convex nonlinearity
Indefinite sublinear nonlinearity
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Summary:We are concerned with existence, nonexistence and multiplicity of nonnegative solutions for the elliptic problem − Δ u = a ( x ) u q + λ b ( x ) u p in Ω , u = 0 on ∂ Ω , where Ω is a bounded domain in R N , λ ∈ R , 0 < q < 1 < p ⩽ 2 ⁎ − 1 and a, b are bounded functions, with b ( x ) ⩾ 0 and a ( x ) changes its sign.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2011.07.002