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- W2156863802 abstract "Synopsis We consider the positive solutions to the semilinear equation: where Ω denotes a smooth bounded region in ℝ N ( N > 1) and ℷ 0. Here f :[0, ∞)→ℝ is assumed to be monotonically increasing, concave and such that f (0)<0 (semipositone). Assuming that f ′(∞)≡lim t→∞ f ( t )> 0, we establish the stability and uniqueness of large positive solutions in terms of ( f ( t )/ t )′ When Ω is a ball, we determine the exact number of positive solutions for each λ > 0. We also obtain the geometry of the branches of positive solutions completely and establish how they evolve. This work extends and complements that of [3, 7] where f ′(∞)≦0." @default.
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- W2156863802 date "1997-01-01" @default.
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- W2156863802 title "Positive solution curves of semipositone problems with concave nonlinearities" @default.
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- W2156863802 doi "https://doi.org/10.1017/s0308210500026809" @default.
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