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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

Citation and License

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