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EIGENVALUE PROBLEMS FOR SINGULAR ODES

  • DONAL O'REGAN (a1) and ALEKSANDRA ORPEL (a2)
Abstract
Abstract

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.

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References
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1.Agarwal R. P. and O'Regan D., Singular differential and integral equations with applications (Kluwer Academic Publisher, Dordrecht, 2003).
2.Agarwal R. P. and O'Regan D., Twin solutions to singular Dirichlet problems, J. Math. Anal. Appl. 240 (1999), 433445.
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.
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.
5.O'Regan D., Theory of singular boundary value problems (World Scientific, Singapore, 1994).
6.Orpel A., On the existence of bounded positive solutions for a class of singular BVP, Nonlinear Anal. 69 (2008), 13891395.
7.Orpel A., Nonlinear BVPS with functional parameters, J. Differ. Equ. 246 (2009), 15001522.
8.Lü 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.
9.Lü 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.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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