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Bounds for solutions of a differential inequality

Author(s): Uri Elias
Journal: Proc. Amer. Math. Soc. 128 (2000), 475-484.
MSC (1991): Primary 34C10
Posted: May 27, 1999
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Abstract: This work compares the solutions of an $n$th order differential inequality plus $n$ boundary conditions with the solution of the related differential equation with $ n-1 $ boundary conditions. The differential operator is assumed to be disconjugate. It is proved that under suitable conditions the ratio of these solutions is monotone. The solution of the inequality can be replaced by the corresponding Green's function.

References:

[Cop]
Coppel, W. A., Disconjugacy, Lecture Notes in Math., vol. 220, Springer Verlag, Berlin, 1971. MR 57:778

[ErW]
Erbe, L. H. and Wang, H., On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994), 743-748. MR 94e:34025

[EHW]
Erbe, L. H., Hu, S., and Wang, H., Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl. 184 (1994), 640-648. MR 95f:34023

[Eli]
Elias, U., Oscillation theory of two-term differential equations, Kluwer Academic Publishers, Dordrecht, 1997. MR 98e:34058

[EH1]
Eloe, P. W. and Henderson, J., Inequalities based on a generalization of concavity, Proc. Amer. Math. Soc. 125 (1997), 2103-2107. MR 97i:34018

[EH2]
Eloe, P. W. and Henderson, J., Inequalities for solutions of multipoint boundary value problems, preprint.

[EH3]
Eloe, P. W. and Henderson, J., Positive solutions and nonlinear $ (k,n-k) $ conjugate eigenvalue problems, Diff. Equ. Dyn. Sys., in press.

[EH4]
Eloe, P. W. and Henderson, J., Positive solutions and nonlinear multipoint conjugate eigenvalue problems, Electronic J. of Diff. Equ. 1997 (1997), 1-11. MR 97j:34023

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Additional Information:

Uri Elias
Affiliation: Department of Mathematics, Technion, Haifa 32000, Israel
Email: elias@tx.technion.ac.il

DOI: 10.1090/S0002-9939-99-05140-0
PII: S 0002-9939(99)05140-0
Keywords: Differential inequality, disconjugate differential operator
Received by editor(s): March 25, 1998
Posted: May 27, 1999
Communicated by: Hal L. Smith
Copyright of article: Copyright 1999, American Mathematical Society

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