Positive solutions for nonlocal fourth-order boundary value problems with all order derivatives
1 College of Electrical Engineering and Information, Hebei University of Science and Technology, Shijiazhuang 050018, Hebei, P. R. China
2 College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, Hebei, P. R. China
Boundary Value Problems 2012, 2012:29 doi:10.1186/1687-2770-2012-29Published: 2 March 2012
In this article, by the fixed point theorem in a cone and the nonlocal fourth-order BVP's Green function, the existence of at least one positive solution for the nonlocal fourth-order boundary value problem with all order derivatives
is considered, where f is a nonnegative continuous function, λ > 0, 0 < A < π2, p, q ∈ L[0, 1], p(s) ≥ 0, q(s) ≥ 0. The emphasis here is that f depends on all order derivatives.