Positive Solutions of a Nonlinear Three-Point Integral Boundary Value Problem. (20th September 2010) - Tariboon Tariboon, Jessada Jessada; Sitthiwirattham Sitthiwirattham, Thanin Thanin
Abstract : We study the existence of positive solutions to the three-point integral boundary value problem u ′′ + a ( t ) f ( u ) = 0, t ∈ ( 0, 1 ), u ( 0 ) = 0, α ∫ 0 η u ( s ) d s = u ( 1 ), where 0 < η < 1 and 0 < α < 2 / η 2 . We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.