Multiple Positive Solutions of Third-Order BVP with Advanced Arguments and Stieltjes Integral Conditions - Jian Chang; Jian-Ping Sun; Ya-Hong Zhao (Journal of Function Spaces)
We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions: u′′′t+ft,uαt=0,  t∈0,1,  u0=γuη1+λ1u and u′′0=0,  u1=βuη2+λ2u, 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.