Existence and Uniqueness of Positive Solution for a Singular Nonlinear Second-Order m-Point Boundary Value Problem. (31st March 2010) - Lv, Xuezhe; Pei, Minghe
Abstract : The existence and uniqueness of positive solution is obtained for the singular second-orderm -point boundary value problemu ′′ ( t ) + f ( t, u ( t ) ) = 0 fort ∈ ( 0, 1 ), u ( 0 ) = 0, u ( 1 ) = ∑ i = 1 m - 2 α i u ( η i ), wherem ≥ 3, α i > 0 ( i = 1, 2, …, m - 2 ), 0 < η 1 < η 2 < ⋯ < η m - 2 < 1 are constants, andf ( t, u ) can have singularities fort = 0 and/ort = 1 and foru = 0 . The main tool is the perturbation technique and Schauder fixed point theorem.