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Boundary value problems singular in the solution variable with nonlinear boundary data

Published online by Cambridge University Press:  20 January 2009

Donal O'Regan
Donal O'Regan
Affiliation:
Department of Mathematics University College Galway Ireland
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Abstract

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Existence results are established for the equation y″ + f(t, y) = 0, 0<t<1. Here f may be singular in y and f is allowed to change sign. Our boundary data include y(0) = y′(1) + ky(1) = 0, k> – 1 and y(0) = y′(1) + cy4(1) = 0, c>0.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 39 , Issue 3 , October 1996 , pp. 505 - 523
Copyright
Copyright © Edinburgh Mathematical Society 1996

References

REFERENCES

1. Baxley, J. V., A singular nonlinear boundary value problem: membrane response of a spherical cap, SIAM J. Appl. Math. 48 (1988), 497–505.CrossRefGoogle Scholar
2. Bobisud, L. E., Calvert, J. E. and Royalty, W. D., Some existence results for singular boundary value problems, Differential Integral Equations 6 (1993), 553–571.CrossRefGoogle Scholar
3. Bobisud, L. E., O'Regan, D. and Royalty, W. D., Solvability of some nonlinear boundary value problems, Nonlinear Anal. 12 (1988), 855–869.CrossRefGoogle Scholar
4. Gatica, J. A., Oliker, V. and Waltman, P., Singular nonlinear boundary value problems for second order ordinary differential equations, J. Differential Equations 79 (1989), 62–78.CrossRefGoogle Scholar
5. Granas, A., Guenther, R. B. and Lee, J. W., Some general existence principles in the Carathéodory theory of nonlinear differential systems. J. Math. Pures Appl. 70 (1991), 153–196.Google Scholar
6. Habets, P. and Zanolin, F., Upper and lower solutions for a generalized Emden-Fowler equation, J. Math. Anal. Appl. 181 (1994), 684–700.CrossRefGoogle Scholar
7. Luning, C. D. and Perry, W. L., Iterative solutions of negative exponent Emden-Fowler problems, Internat. J. Math. Sci. 13 (1990), 159–164.CrossRefGoogle Scholar
8. Mooney, J. W., Solution of a Thomas-Fermi problem using linear approximants, Comput. Phys. Comm. 96 (1993), 51–57.CrossRefGoogle Scholar
9. Na, T. Y., Computational methods in engineering boundary value problems (Academic Press, New York, 1979).Google Scholar
10. O'Regan, D., Positive solutions to singular boundary value problems with at most linear growth, Appl. Anal. 49 (1993), 171–196.CrossRefGoogle Scholar
11. O'Regan, D., Theory of singular boundary value problems (World Scientific, Singapore, 1994).CrossRefGoogle Scholar
12. Taliaferro, S., A nonlinear singular boundary value problem, J. Nonlinear Anal. 3 (19790), 897–904.CrossRefGoogle Scholar