Positive solution curves of an infinite semipositone problem
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In this article we consider the infinite semipositone problem -∆u = λƒ(u) in Ω, a smooth bounded domain in ℝN, and u = 0 on ∂Ω, where ƒ(t) = tq - t-β and 0 < q, β < 1. Using stability analysis we prove the existence of a connected branch of maximal solutions emanating from infinity. Under certain additional hypothesis on the extremal solution at λ = Λ we prove a version of Crandall-Rabinowitz bifurcation theorem which provides a multiplicity result for λ ∈ (Λ, Λ + ε).
CitationDhanya, R. (2018). Positive solution curves of an infinite semipositone problem. Electronic Journal of Differential Equations, 2018(178), pp. 1-14.
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