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Open Access Research

Monotone and convex positive solutions for fourth-order multi-point boundary value problems

Yang Liu12*, Zhang Weiguo1 and Shen Chunfang2

Author affiliations

1 College of Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China

2 Department of Mathematics, Hefei Normal University, Hefei, Anhui Province 230061, PR China

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Citation and License

Boundary Value Problems 2011, 2011:21  doi:10.1186/1687-2770-2011-21

Published: 5 September 2011

Abstract

The existence results of multiple monotone and convex positive solutions for some fourth-order multi-point boundary value problems are established. The nonlinearities in the problems studied depend on all order derivatives. The analysis relies on a fixed point theorem in a cone. The explicit expressions and properties of associated Green's functions are also given.

MSC: 34B10; 34B15.

Keywords:
multi-point boundary value problem; positive solution; cone; fixed point