School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China.
*Corresponding author, E-mail: hrsun@lzu.edu.cn.
AMS subject classification: 34B16, 47H11.
The singular nonlinear three-point boundary value problems are discussed under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, where (Lu)(t) = (p(t)u’(t))’+q(t)u(t), 0 < η < 1, h(t) is allowed to be singular at both t = 0 and t = 1, and f need not be non-negative. The associated Green function for the problem is first given, and some existence criteria of nontrivial solutions and positive solutions are established by using topological degree theory.
Three-point boundary value problems, Green's function, nontrivial solution, positive solution, topological degree
