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- W2027187949 abstract "We consider the existence of positive solutions of the singular nonlinear semipositone problem of the form $left{ begin{gathered} - div(|x|^{ - alpha p} |nabla u|^{p - 2} nabla u) = |x|^{ - (alpha + 1)p + beta } left( {au^{p - 1} - f(u) - frac{c} {{u^gamma }}} right),x in Omega , hfill u = 0,x in partial Omega , hfill end{gathered} right. $ where Ω is a bounded smooth domain of ℝ N with 0 ∈ Ω, 1 < p < N, 0 ⩽ α < (N − p)/p, γ ∈ (0, 1), and a, β, c and λ are positive parameters. Here f: [0,∞) → ℝ is a continuous function. This model arises in the studies of population biology of one species with u representing the concentration of the species. We discuss the existence of a positive solution when f satisfies certain additional conditions. We use the method of sub-supersolutions to establish our results." @default.
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- W2027187949 date "2014-06-01" @default.
- W2027187949 modified "2023-10-02" @default.
- W2027187949 title "A population biological model with a singular nonlinearity" @default.
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- W2027187949 doi "https://doi.org/10.1007/s10492-014-0053-7" @default.
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