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Boundary value problems on noncompact intervals

Published online by Cambridge University Press:  14 November 2011

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

Existence results are established for second-order boundary value problems for ordinary differential equations on non-compact intervals.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 4 , 1995 , pp. 777 - 799
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Atkinson, F. V. and Peletier, L. A.. Similarity profiles of flows through porous media. Arch. Rational Mech. Anal. 42 (1971), 369–79.Google Scholar
2Atkinson, F. V. and Peletier, L. A.. Similarity solutions of the nonlinear diffusion equation. Arch. Rational Mech. Anal. 54 (1974), 373–92.Google Scholar
3Baxley, J. V.. Existence and uniqueness for nonlinear boundary value problems on infinite intervals. J. Math. Anal. Appl. 147 (1990), 122–33.Google Scholar
4Berbernes, J. W. and Jackson, L. K.. Infinite interval boundary value problems for y˝ = f(t, y), Duke Math. J. 34 (1967), 39–47.Google Scholar
5Chan, C. Y. and Hon, Y. C.. Computational methods for generalised Emden-Fowler models of neutral atoms. Quart. Appl. Math. 46 (1988), 711–26.Google Scholar
6Dugundji, J. and Granas, A.. Fixed point theory. Monograf. Mat. (Warsaw: PWN, 1982).Google Scholar
7Frigon, M.. Application de la théorie de la transversalité topologique à des problèmes nonlinéaires pour des équations différentielles ordinaires. Dissertationes Math. 296 (1990), 1–79.Google Scholar
8Furi, M. and Pera, P.. A continuous method on locally convex spaces and applications to ordinary differential equations on noncompact intervals. Ann. Polon. Math. 47 (1987), 331–46.Google Scholar
9Granas, 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), 153–96.Google Scholar
10Granas, A., Guenther, R. B., Lee, J. W. and O'Regan, D.. Boundary value problems on infinite intervals and semiconductor devices. J. Math. Anal. Appl. 116 (1986), 335–48.CrossRefGoogle Scholar
11Okrasinski, W.. On a nonlinear ordinary differential equation. Ann. Polon. Math. 49 (1989), 237–45.Google Scholar
12O'Regan, D.. Singular boundary value problems on the semi infinite interval. Libertas Math. 12 (1992), 109–19.Google Scholar
13O'Regan, D.. Existence theory for the equations (G´(y))´ = qf(t, y, y´) and (G´(y) – pH(y))´ = -p´H(y) + qf(t, y). J. Math. Anal. Appl. 183 (1994), 263–84.Google Scholar
14O'Regan, D.. Positive solutions for a class of boundary value problems on infinite intervals. Nonlinear Differential Equations Appl. 1 (1994), 203–28.Google Scholar
15Przeradzki, B.. On the solvability of singular boundary value problems for second order ordinary differential equations. Ann. Polon Math. 50 (1990), 279–89.Google Scholar
16Schmidt, K. and Thompson, R.. Boundary value problems for infinite systems of second order differential equations. 18 (1975), 277–95.Google Scholar
17Torchinsky, A.. Real Variables (Reading, MA: Addison-Wesley, 1988).Google Scholar