Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions

We consider the following third-order boundary value problem with advanced arguments and stieltjes integral boundary conditions: u″′(t) + f(t,u(α(t))) = 0,t ∈ (0,1),u (0) = γu(η1) + λ1[u] and u″(0) = 0,u(1) = βu(η2) + λ2[u],where 0 < η1 < η2 < 1,0 ≤ γ,β ≤ 1,α: [0,1] → [0,1] is continuous,α(t) ≥ t for t ∈ [0,1],and α(t) ≤ η2 for t ∈ [η1,η2]. under some suitable conditions,by applying a fixed point theorem due to avery and peterson,we obtain the existence of multiple positive solutions to the above problem. an example is also included to illustrate the main results obtained. � 2016 jian chang et al.