Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-29T06:31:28.813Z Has data issue: false hasContentIssue false
  • English
  • Français

Positive solutions of singular nonlinear Sturm-Liouville boundary value problems

Published online by Cambridge University Press:  17 February 2009

Yan Sun ,
Lishan Liu  and
Yeol Je Cho
Yan Sun
Affiliation:
Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165, P. R. China; e-mail: ysun@163169.net, lls@qfnu.edu.cn.
Lishan Liu
Affiliation:
Department of Mathematics, Qufu Normal University, Qufu, Shandong 273165, P. R. China; e-mail: ysun@163169.net, lls@qfnu.edu.cn.
Yeol Je Cho
Affiliation:
Department of Mathematics Education, The Research Institute of Natural Sciences, College of Education, Gyeongsang National University, Chinju 660-701, Korea; e-mail: yjcho@nongae.gsnu.ac.kr.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

By using fixed point index theory, we present the existence of positive solutions for a Sturm-Liouville singular boundary value problem with at least one positive solution. Our results significantly extend and improve many known results even for non-singular cases.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 4 , April 2004 , pp. 557 - 571
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Agarwal, R. P. and O'Regan, D., “Positive solutions to superlinear singular boundary value problems”, J. Comput. Appl. Math. 88 (1998) 129–147.CrossRefGoogle Scholar
[2]Cheng, J. G. and Zhang, Z. J., “On the existence of positive solutions for a class of singular boundary value problems”, Nonlinear Anal. 44 (2001) 645–655.CrossRefGoogle Scholar
[3]Dalmasso, R., “Positive solutions of singular boundary value problems”, Nonlinear Anal. 27 (1996) 645–652.CrossRefGoogle Scholar
[4]Erbe, L. H. and Wang, H., “On the existence of positive solutions of ordinary differential equations”, Proc. Amer. Math. Soc. 120 (1994) 743–748.CrossRefGoogle Scholar
[5]Guo, D. and Lakshmikantham, V., Nonlinear problems in abstract cones (Academic Press, San Diego, 1988).Google Scholar
[6]Ha, K. S. and Lee, Y. H., “Existence of multiple positive solutions of singular boundary value problems”, Nonlinear Anal. 28 (1997) 1429–1438.CrossRefGoogle Scholar
[7]Henderson, J. and Wang, H., “Positive solutions for nonlinear eigenvalue problems”, J. Math. Anal. Appl. 208 (1997) 252–259.CrossRefGoogle Scholar
[8]Lan, K. Q. and Webb, J., “Positive solutions of semilinear differential equations with singularities“, J. Differential Equations 148 (1998) 407–421.CrossRefGoogle Scholar
[9]Li, R. G. and Liu, L. S., “Positive solutions of boundary value problems for second-order singular nonlinear differential equations”, Appl. Math. Mech. 22 (2001) 495–500.CrossRefGoogle Scholar
[10]Ma, R. Y., “Positive solutions of singular second-order boundary-value problems”, Acta Math. Sinica (N.S.) 14 (1998) 691–698.Google Scholar
[11]O'Regan, D., “Singular second-order boundary-value problems”, Nonlinear Anal. 15 (1990) 1097–1109.CrossRefGoogle Scholar
[12]Zhang, Y., “Positive solutions of singular sublinear Emden-Fowler boundary value problems”, J. Math. Anal. Appl. 185 (1994) 215–222.CrossRefGoogle Scholar