Existence and Global Asymptotic Behavior of Singular Positive Solutions for Radial Laplacian. (3rd February 2019) - Bachar, Imed; Mâagli, Habib; Mesloub, Said
Abstract : The aim of this paper is to establish existence and uniqueness of a positive continuous solution to the following singular nonlinear problem.{ - t 1 - n t n - 1 u ′ ′ = a ( t ) u σ,     t ∈ ( 0, 1 ),     lim t → 0 ⁡ t n - 1 u ′ ( t ) = 0,     u ( 1 ) = 0 }, wheren ≥ 3, σ < 1, anda denotes a nonnegative continuous function that might have the property of being singular att = 0 and /ort = 1 and which satisfies certain condition associated to Karamata class. We emphasize that the nonlinearity might also be singular atu = 0, while the solution could blow-up at0 . Our method is based on the global estimates of potential functions and the Schauder fixed point theorem.