Uniqueness and Parameter Dependence of Positive Solution of Fourth-Order Nonhomogeneous BVPs. (28th July 2010) - Sun Sun, Jian-Ping Jian-Ping; Wang Wang, Xiao-Yun Xiao-Yun
Abstract : We investigate the following fourth-order four-point nonhomogeneous Sturm-Liouville boundary value problem: u ( 4 ) = f ( t, u ), t ∈ [ 0, 1 ], α u ( 0 ) − β u ′ ( 0 ) = λ 1, γ u ( 1 ) + δ u ′ ( 1 ) = λ 2, a u ′′ ( ξ 1 ) − b u ′′′ ( ξ 1 ) = − λ 3, c u ′′ ( ξ 2 ) + d u ′′′ ( ξ 2 ) = − λ 4, where 0 ≤ ξ 1 < ξ 2 ≤ 1 and λ i ( i = 1, 2, 3, 4 ) are nonnegative parameters. Some sufficient conditions are given for the existence and uniqueness of a positive solution. The dependence of the solution on the parameters λ i ( i = 1, 2, 3, 4 ) is also studied.