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

• Published in: Boundary value problems Vol. 2012; no. 1; pp. 1 - 16
• Main Author: Sun, Yan
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 09.02.2012; Hindawi Limited; BioMed Central Ltd
• Subjects: Analysis; Approximation; Approximations and Expansions; Boundary value problems; Classification; Derivatives; Difference and Functional Equations; Integrals; Mathematical analysis; Mathematics; Mathematics and Statistics; Nonlinearity; Operators; Ordinary Differential Equations; Partial Differential Equations; positive solutions; semipositone; multi-point boundary value problems
• ISSN: 1687-2770; 1687-2762; 1687-2770
• DOI: 10.1186/1687-2770-2012-12

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.