Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T03:14:37.380Z Has data issue: false hasContentIssue false
  • English
  • Français

Existence theory for nonresonant singular boundary value problems

Published online by Cambridge University Press:  20 January 2009

Donal O'Regan
Donal O'Regan
Affiliation:
Department of Mathematics, University College Galway, Galway, Ireland
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 present some existence results for the “nonresonant” singular boundary value problem a.e. on [0, 1] with Here μ is such that a.e. on [0, 1] with has only the trivial solution.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 3 , October 1995 , pp. 431 - 447
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

REFERENCES

1.Atkinson, F. V., Discrete and continuous boundary problems (Academic Press, New York, 1964).Google Scholar
2.Bobisud, L. E. and O'regan, D., Positive solutions for a class of nonlinear singular boundary value problems at resonance, J. Math. Anal. Appl 184 (1994), 263–284.CrossRefGoogle Scholar
3.Chambre, P. L., On the solution of the Poisson-Boltzmann equation with application to the theory of thermal explosions, J. Chem. Phys. 20 (1952), 1795–1797.CrossRefGoogle Scholar
4.Chawla, M. M. and Shivakumar, P. N., On the existence of solutions of a class of singular nonlinear two point boundary value problems, J. Comput. Appl. Math. 19 (1987), 379–388.CrossRefGoogle Scholar
5.Dunninger, D. R. and Kurtz, J. C., A priori bounds and existence of positive solutions for singular nonlinear boundary value problems, SIAM J. Math. Anal. 17 (1986), 595–609.CrossRefGoogle Scholar
6.El-Gebeily, M. A., Boumenir, A. and Elgindi, A. B. M., Existence and uniqueness of solutions of a class of two-point singular nonlinear boundary value problems, J. Comput. Appl. Math., 46 (1993), 345–355.CrossRefGoogle Scholar
7.Fonda, A. and Mawhin, J., Quadratic forms, weighted eigenfunctions and boundary value problems for nonlinear second order differential equations, Proc. Royal Soc. Edinburgh 112A (1989), 145–153.CrossRefGoogle Scholar
8.Frigon, M. and O'regan, D., Some general existence principles for ordinary differential equations, Topotogical Methods in Nonlinear Anal. 2 (1993), 35–54.CrossRefGoogle Scholar
9.Granas, A., Guenther, R. B. and Lee, J. W., Some general existence principles in the Caratheodory theory of nonlinear differential systems, J. Math. Pares Appl. 70 (1991), 153–196.Google Scholar
10.Iannacci, R. and Nkashama, M. N., Nonlinear two-point boundary value problems at resonance without Landesman-Lazer condtions, Proc. Amer. Math. Soc. 106 (1989), 943–952.Google Scholar
11.Keller, J. B., Electrodynamics I. The equilibrium of a charged gas in a container, J. Rat. Mech. Anal. 5 (1957), 715–724.Google Scholar
12.Krasnoselskii, M. A., Topological methods in the theory of nonlinear integral equations (MacMillan Co., New York, 1964).Google Scholar
13.Mawhin, J., Ward, J. R. and Willem, M., Necessary and sufficient conditions for the solvability of a nonlinear two point boundary value problem, Proc. Amer. Math. Soc. 93 (1985), 667–674.CrossRefGoogle Scholar
14.Mawhin, J. and Omano, W., Two point boundary value problems for nonlinear perturbations of some singular linear differential equations at resonance, Comment. Math. Univ. Carolina. 30 (1989), 537–550.Google Scholar
15.Mooney, J. W., Numerical schemes for degenerate boundary value problems, J. Phys. A. 26 (1993), 413–421.CrossRefGoogle Scholar
16.Naimark, M. A., Linear differential operators Part II (Ungar Publ. Co., London, 1968).Google Scholar
17.O'regan, D., Solvability of some two point boundary value problems of Dirichlet, Neumann or Periodic type, Dynamic Systems and Appl. 2 (1993), 163–182.Google Scholar
18.O'regan, D., Singular Sturm Liouville problems and existence of solutions to singular nonlinear boundary value problems, Nonlinear Anal. 20 (1993), 767–779.CrossRefGoogle Scholar
19.O'regan, D., Existence theory for singular two point boundary value problems, in Proc. Fourth Int. Coll. Diff. Eq. (Plovdiv, Bulgaria, Int. Science Publ., Utrecht, 1994), 215–228.Google Scholar
20.O'regan, D., Existence principles for second order nonresonant boundary value problems, J. Appl. Math. Stoch. Anal. 7 (1994), 487–507.CrossRefGoogle Scholar
21.O'regan, D., Nonresonant and resonant singular boundary value problems, to appear.Google Scholar
22.Powers, D., Boundary value problems (Harcourt Brace Jovanovich, San Diego, 1987).Google Scholar
23.Sanchez, L., Positive solutions for a class of semilinear two point boundary value problems, Bull. Austral. Math. Soc. 45 (1992), 439–451.CrossRefGoogle Scholar
24.Stakgold, I., Greens functions and boundary value problems (John Wiley and Sons, New York, 1979).Google Scholar