SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Positive solutions for the third-order boundary value problems with the second derivatives

Yanping Guo1, Yujing Liu2 and Yonhchun Liang1*

Author Affiliations

1 College of Electrical Engineering and Information, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, PR China

2 College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, Hebei, PR China

For all author emails, please log on.

Boundary Value Problems 2012, 2012:34  doi:10.1186/1687-2770-2012-34

Published: 26 March 2012

Abstract

By using the fixed-point index theory in a cone and defining a linear operator, we obtain the existence of at least one positive solution for the third-order boundary value problem with integral boundary conditions

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/34/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/34/mathml/M1">View MathML</a>

where f : [0, 1] × R+ × R- → R+ is a nonnegative function. The associated Green's function for the above problem is also used, and a new reproducing cone also used.

Keywords:
fixed-point index theory; Green's function; positive solution; boundary value problem