School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000, People's Republic of China. E-mail: hrsun@lzu.edu.cn
†Corresponding author.
* Supported by the NNSF of China (10571078), China Postdoctoral Science Foundation and the Fundamental Research Fund for Physics and Mathematic of Lanzhou University
In this paper, we consider the nonlinear third order ordinary differential equation u″′(t) = λa(t)f(u(t)), 0 < t < 1 with the boundary conditions αu′(0)–βu″(0) = 0, u(1) = 0. Some sufficient conditions for the nonexistence and existence of at least one, two and n positive solutions for the boundary value problem are established. In doing so the usual restriction that and exist is removed. An example is also given to illustrate the main results.
Boundary value problem, third order, positive solution, fixed point theorem.
