Iteration for a Third-Order Three-Point BVP with Sign-Changing Green's Function

作者：Zhao, Ya-Hong^*; Li, Xing-Long

来源：Journal of Applied Mathematics, 2014, 2014: 541234.

DOI：10.1155/2014/541234

• POSITIVE SOLUTIONS
• EXISTENCE

We are concerned with the following third-order three-point boundary value problem: u"'(t) = f(t,u(t)), t is an element of [0, 1], u'(0) = u(1) = 0, u ''(eta) + alpha u(0) = 0, where alpha is an element of [0,2) and eta is an element of [2/3, 1). Although corresponding Green's function is sign-changing, we still obtain the existence of monotone positive solution under some suitable conditions on f by applying iterative method. An example is also included to illustrate the main results obtained.

• 单位
  兰州理工大学