Open Access

Positive Solutions for Two-Point Semipositone Right Focal Eigenvalue Problem

Boundary Value Problems20072007:023108

DOI: 10.1155/2007/23108

Received: 28 March 2007

Accepted: 27 August 2007

Published: 17 October 2007


Krasnoselskii's fixed-point theorem in a cone is used to discuss the existence of positive solutions to semipositone right focal eigenvalue problems , , , , , where , is fixed, is continuous with for some positive constant .


Authors’ Affiliations

Department of Mathematics, Bei Hua University


  1. Agarwal RP: Boundary Value Problems for Higher Order Differential Equations. World Scientific, Singapore; 1986:xii+307.MATHView ArticleGoogle Scholar
  2. Agarwal RP, O'Regan D, Lakshmikantham V: Singular focal and higher order boundary value problems. Nonlinear Analysis: Theory, Methods & Applications 2000,42(2):215–228. 10.1016/S0362-546X(98)00341-1MATHMathSciNetView ArticleGoogle Scholar
  3. Boey KL, Wong PJY: Two-point right focal eigenvalue problems on time scales. Applied Mathematics and Computation 2005,167(2):1281–1303. 10.1016/j.amc.2004.09.007MATHMathSciNetView ArticleGoogle Scholar
  4. He X, Ge W: Positive solutions for semipositone right focal boundary value problems. Applicable Analysis 2002,81(2):227–240. 10.1080/0003681021000021943MATHMathSciNetView ArticleGoogle Scholar
  5. Ma R: Multiple positive solutions for a semipositone fourth-order boundary value problem. Hiroshima Mathematical Journal 2003,33(2):217–227.MATHMathSciNetGoogle Scholar
  6. Wong PJY, Agarwal RP: Multiple positive solutions of two-point right focal boundary value problems. Mathematical and Computer Modelling 1998,28(3):41–49. 10.1016/S0895-7177(98)00097-1MATHMathSciNetView ArticleGoogle Scholar
  7. Wong PJY, Agarwal RP: On two-point right focal eigenvalue problems. Zeitschrift für Analysis und ihre Anwendungen 1998,17(3):691–713.MATHMathSciNetView ArticleGoogle Scholar
  8. Agarwal RP, Wong F-H: Existence of positive solutions for non-positive higher-order BVPs. Journal of Computational and Applied Mathematics 1998,88(1):3–14. 10.1016/S0377-0427(97)00211-2MATHMathSciNetView ArticleGoogle Scholar


© Y. Lin and M. Pei 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.