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

作者：Chang, Jian; Sun, Jian-Ping^*; Zhao, Ya-Hong

来源：Journal of Function Spaces, 2016, 2016: 3805804.

DOI：10.1155/2016/3805804

• BOUNDARY-VALUE-PROBLEMS
• EXISTENCE

We consider the following third-order boundary value problem with advanced arguments and Stieltjes integral boundary conditions u''' (t) + f(t,u(alpha(t))) = 0, t is an element of(0, 1), u(0) = gamma u(eta(1)) + lambda(1)[u] and u '' (0) = 0, u(1) = beta u(eta(2)) + lambda(2)[u], where 0 < eta(1) < eta(2) < 1, 0 <= gamma, beta <= 1, alpha : [0, 1] -> [0, 1] is continuous, alpha(t) >= t for t is an element of [0, 1], and alpha (t) <= eta(2) for t is an element of [eta(1), eta(2)]. 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.

• 出版日期2016
• 单位兰州理工大学