Open Access Research

The existence and multiplicity of positive solutions of nonlinear sixth-order boundary value problem with three variable coefficients

Wanjun Li

Author Affiliations

Department of Mathematics, Longdong University, Qingyang 745000, Gansu, P. R. China

Boundary Value Problems 2012, 2012:22  doi:10.1186/1687-2770-2012-22

Published: 22 February 2012

Abstract

In this article, we discuss the existence and multiplicity of positive solutions for the sixth-order boundary value problem with three variable parameters as follows:

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/22/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/22/mathml/M1">View MathML</a>

where A(t), B(t), C(t) ∈ C[0,1], f(t, u) : [0,1] × [0, ∞) → [0. ∞) is continuous. The proof of our main result is based upon spectral theory of operators and fixed point theorem in cone.

Keywords:
sixth-order differential equation; positive solution; fixed point theorem; spectral theory of operators