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