Open Access Research

Existence of positive solutions for fourth-order semipositone multi-point boundary value problems with a sign-changing nonlinear term

Yan Sun

Author Affiliations

Department of Mathematics, Shanghai Normal University, Shanghai 200234, People's Republic of China

Boundary Value Problems 2012, 2012:12  doi:10.1186/1687-2770-2012-12

Published: 9 February 2012

Abstract

In this article, some new sufficient conditions are obtained by making use of fixed point index theory in cone and constructing some available integral operators together with approximating technique. They guarantee the existence of at least one positive solution for nonlinear fourth-order semipositone multi-point boundary value problems. The interesting point is that the nonlinear term f not only involve with the first-order and the second-order derivatives explicitly, but also may be allowed to change sign and may be singular at t = 0 and/or t = 1. Moreover, some stronger conditions that common nonlinear term f ≥ 0 will be modified. Finally, two examples are given to demonstrate the validity of our main results.

2000 Mathematics Subject Classification: 34B10; 34B18; 47N20.

Keywords:
semipositone; positive solutions; multi-point boundary value problems