Positive solutions for third order multi-point singular boundary value problems

John R. Graef; Lingju Kong; Bo Yang

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 1, page 173-182
  • ISSN: 0011-4642

Abstract

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We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.

How to cite

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Graef, John R., Kong, Lingju, and Yang, Bo. "Positive solutions for third order multi-point singular boundary value problems." Czechoslovak Mathematical Journal 60.1 (2010): 173-182. <http://eudml.org/doc/37999>.

@article{Graef2010,
abstract = {We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.},
author = {Graef, John R., Kong, Lingju, Yang, Bo},
journal = {Czechoslovak Mathematical Journal},
keywords = {positive solution; singular boundary value problem; multi-point boundary condition; nonlinear alternative of Leray-Schauder; positive solution; singular boundary value problem; multi-point boundary condition; nonlinear alternative of Leray-Schauder},
language = {eng},
number = {1},
pages = {173-182},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Positive solutions for third order multi-point singular boundary value problems},
url = {http://eudml.org/doc/37999},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Graef, John R.
AU - Kong, Lingju
AU - Yang, Bo
TI - Positive solutions for third order multi-point singular boundary value problems
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 1
SP - 173
EP - 182
AB - We study a third order singular boundary value problem with multi-point boundary conditions. Sufficient conditions are obtained for the existence of positive solutions of the problem. Recent results in the literature are significantly extended and improved. Our analysis is mainly based on a nonlinear alternative of Leray-Schauder.
LA - eng
KW - positive solution; singular boundary value problem; multi-point boundary condition; nonlinear alternative of Leray-Schauder; positive solution; singular boundary value problem; multi-point boundary condition; nonlinear alternative of Leray-Schauder
UR - http://eudml.org/doc/37999
ER -

References

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  1. Agarwal, R. P., O'Regan, D., Singular Differential and Integral Equations with Applications, Kluwer Academic Publishers, Boston (2003). (2003) Zbl1055.34001MR2011127
  2. Agarwal, R. P., O'Regan, D., 10.1006/jdeq.1998.3501, J. Differential Equations 150 (1998), 462-473. (1998) Zbl0920.34027MR1658664DOI10.1006/jdeq.1998.3501
  3. Agarwal, R. P., O'Regan, D., 10.1006/jdeq.1996.0147, J. Differential Equations 130 (1996), 333-355. (1996) Zbl0863.34022MR1410892DOI10.1006/jdeq.1996.0147
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  6. Graef, J. R., Henderson, J., Yang, B., Positive solutions to a singular third order nonlocal boundary value problem, Indian J. Math. 50 (2008), 317-330. (2008) Zbl1168.34317MR2517736
  7. Graef, J. R., Henderson, J., Yang, B., Existence of positive solutions of a higher order nonlocal singular boundary value problem, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16, Supplement S1 (2009), 147-152. (2009) Zbl1180.34020MR2518860
  8. Graef, J. R., Yang, B., Positive solutions of a third order nonlocal boundary value problem, Discrete Contin. Dyn. Syst. Ser. S 1 (2008), 89-97. (2008) Zbl1153.34014MR2375585
  9. Eloe, P. W., Henderson, J., 10.1006/jdeq.1996.3207, J. Differential Equations 133 (1997), 136-151. (1997) Zbl0870.34031MR1426760DOI10.1006/jdeq.1996.3207
  10. Eloe, P. W., Henderson, J., 10.1016/0362-546X(91)90116-I, Nonlinear Anal. 17 (1991), 1-10. (1991) Zbl0731.34015MR1113445DOI10.1016/0362-546X(91)90116-I
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  12. Maroun, M., Positive solutions to an third-order right focal boundary value problem, Comm. Appl. Nonlinear Anal. 12 (2005), 71-82. (2005) MR2142919
  13. Kong, L., Kong, Q., Positive solutions of higher-order boundary value problems, Proc. Edinburgh Math. Soc. 48 (2005), 445-464. (2005) Zbl1084.34023MR2157255
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