Open Access Research

Positive solutions for nonlocal fourth-order boundary value problems with all order derivatives

Yanping Guo1, Fei Yang2 and Yongchun Liang1*

Author affiliations

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

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Citation and License

Boundary Value Problems 2012, 2012:29  doi:10.1186/1687-2770-2012-29

Published: 2 March 2012

Abstract

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

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/29/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/29/mathml/M1">View MathML</a>

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.

Keywords:
fourth-order boundary value problem; fixed point theorem; Green's function; positive solution