Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-26T01:41:35.675Z Has data issue: false hasContentIssue false

EIGENVALUE PROBLEMS FOR SINGULAR ODES

Published online by Cambridge University Press:  09 December 2010

DONAL O'REGAN
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland
ALEKSANDRA ORPEL
Affiliation:
Faculty of Mathematics and Computer Science, University of Lodz, Poland e-mail: [email protected]
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.

We investigate eigenvalue intervals for the Dirichlet problem when the nonlinearity may be singular at t = 0 or t = 1. Our approach is based on variational methods and cover both sublinear and superlinear cases. We also study the continuous dependence of solutions on functional parameters.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Agarwal, R. P. and O'Regan, D., Singular differential and integral equations with applications (Kluwer Academic Publisher, Dordrecht, 2003).CrossRefGoogle Scholar
2.Agarwal, R. P. and O'Regan, D., Twin solutions to singular Dirichlet problems, J. Math. Anal. Appl. 240 (1999), 433445.CrossRefGoogle Scholar
3.Djebali, S. and Orpel, A., A note on positive evanescent solutions for a certain class of elliptic problems, J. Math. Anal. Appl. 353 (2009), 215223.CrossRefGoogle Scholar
4.Nowakowski, A. and Rogowski, A., Multiple positive solutions for a nonlinear Dirichlet problem with nonconvex vector-valued response, Proc. R. Soc. Edinburgh 135A (2005), 105117.CrossRefGoogle Scholar
5.O'Regan, D., Theory of singular boundary value problems (World Scientific, Singapore, 1994).CrossRefGoogle Scholar
6.Orpel, A., On the existence of bounded positive solutions for a class of singular BVP, Nonlinear Anal. 69 (2008), 13891395.CrossRefGoogle Scholar
7.Orpel, A., Nonlinear BVPS with functional parameters, J. Differ. Equ. 246 (2009), 15001522.CrossRefGoogle Scholar
8., H., O'Regan, D. and Agarwal, R. P., An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing nonlinearities, Math. Inequalities Appl. 11 (2007), 8198.Google Scholar
9., H., O'Regan, D. and Agarwal, R. P., Existence to singular boundary value problems with sign changing nonlinearities using an approximation methods approach, Appl. Math. 52 (2007), 117135.CrossRefGoogle Scholar