Open Access Research Article

Positive Solutions for Two-Point Semipositone Right Focal Eigenvalue Problem

Yuguo Lin and Minghe Pei*

Author Affiliations

Department of Mathematics, Bei Hua University, JiLin City 132013, China

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Boundary Value Problems 2007, 2007:023108  doi:10.1155/2007/23108


The electronic version of this article is the complete one and can be found online at: http://www.boundaryvalueproblems.com/content/2007/1/023108


Received:28 March 2007
Revisions received:13 July 2007
Accepted:27 August 2007
Published:17 October 2007

© 2007 Lin and Pei

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.

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 .

References

  1. Agarwal, RP: Boundary Value Problems for Higher Order Differential Equations,p. xii+307. World Scientific, Singapore (1986)

  2. Agarwal, RP, O'Regan, D, Lakshmikantham, V: Singular focal and higher order boundary value problems. Nonlinear Analysis: Theory, Methods & Applications. 42(2), 215–228 (2000). PubMed Abstract | Publisher Full Text OpenURL

  3. Boey, KL, Wong, PJY: Two-point right focal eigenvalue problems on time scales. Applied Mathematics and Computation. 167(2), 1281–1303 (2005). Publisher Full Text OpenURL

  4. He, X, Ge, W: Positive solutions for semipositone right focal boundary value problems. Applicable Analysis. 81(2), 227–240 (2002). Publisher Full Text OpenURL

  5. Ma, R: Multiple positive solutions for a semipositone fourth-order boundary value problem. Hiroshima Mathematical Journal. 33(2), 217–227 (2003)

  6. Wong, PJY, Agarwal, RP: Multiple positive solutions of two-point right focal boundary value problems. Mathematical and Computer Modelling. 28(3), 41–49 (1998). Publisher Full Text OpenURL

  7. Wong, PJY, Agarwal, RP: On two-point right focal eigenvalue problems. Zeitschrift für Analysis und ihre Anwendungen. 17(3), 691–713 (1998). PubMed Abstract OpenURL

  8. Agarwal, RP, Wong, F-H: Existence of positive solutions for non-positive higher-order BVPs. Journal of Computational and Applied Mathematics. 88(1), 3–14 (1998). Publisher Full Text OpenURL