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Abstract Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation.… Click to show full abstract
Abstract Positive singular radial entire solutions of a biharmonic equation with subcritical exponent are obtained via the entire radial solutions of the equation with supercritical exponent and the Kelvin's transformation. The expansions of such singular radial solutions at the singular point 0 are presented. Using these singular radial entire solutions, we construct solutions with a prescribed singular set for the Navier boundary value problem Δ 2 u = u p in Ω , u = Δ u = 0 on ∂ Ω where Ω is a smooth open set of R n with n ≥ 5 .
Journal Title: Journal of Differential Equations
Year Published: 2017
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