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ISSN 1088-6826(e) ISSN 0002-9939(p)

Twin solutions to singular boundary value problems

Author(s): Ravi P. Agarwal; Donal O'Regan
Journal: Proc. Amer. Math. Soc. 128 (2000), 2085-2094.
MSC (1991): Primary 34B15
Posted: February 25, 2000
MathSciNet review: 1664297
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Abstract: In this paper we establish the existence of two nonnegative solutions to singular $\,(n,p)\,$ and singular $\,(p,n-p)\,$ focal boundary value problems. Our nonlinearity $\,f(t,y)\,$ may be singular at $\,y=0$ , $\,t=0\,$ and/or $\,t=1$ .

References:

[1]: R. P. Agarwal and D. O'Regan, Singular boundary value problems for superlinear second order ordinary and delay differential equations, Jour. Differential Eqns., 130(1996), 333-355. MR 97g:34028
[2]: R. P. Agarwal and D. O'Regan, Right focal singular boundary value problems, ZAMM 79(1999), 363-373. CMP 99:14
[3]: R. P. Agarwal, D. O'Regan and V. Lahshmikantham, Singular $\,(p,n-p)\,$ focal and $\,(n,p)\,$ higher order boundary value problems, Nonlinear Analysis, to appear.
[4]: R. P. Agarwal, D. O'Regan and P. J. Y. Wong, Positive solutions of Differential, Difference and Integral equations, Kluwer, Dordrecht, 1999. CMP 99:10
[5]: P. W. Eloe and J. Henderson, Singular nonlinear boundary value problems for higher order ordinary differential equations, Nonlinear Analysis, 17(1991), 1-10. MR 93b:34034
[6]: L. H. Erbe, S. Hu and H. Wang, Multiple positive solutions of some boundary value problems, Jour. Math. Anal. Appl., 184(1994), 640-648. MR 95f:34023
[7]: D. O'Regan, Existence Theory for Nonlinear Ordinary Differential Equations, Kluwer, Dordrecht, 1997. MR 98h:34042

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Additional Information:

Ravi P. Agarwal
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 11926
Email: matravip@nus.edu.sg

Donal O'Regan
Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
Email: donal.oregan@nuigalway.ie

DOI: 10.1090/S0002-9939-00-05320-X
PII: S 0002-9939(00)05320-X
Keywords: Multiple solutions, singular problems, Leray--Schauder alternative, Krasnoselskii's fixed point theorem, lower type inequalities
Received by editor(s): September 1, 1998
Posted: February 25, 2000
Communicated by: Hal L. Smith
Copyright of article: Copyright 2000, American Mathematical Society

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