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Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations
Author(s):
John
R.
Graef;
Chuanxi
Qian;
Bo
Yang
Journal:
Proc. Amer. Math. Soc.
131
(2003),
577-585.
MSC (2000):
Primary 34B15
Posted:
June 18, 2002
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Abstract:
In this paper, the authors consider the boundary value problem
and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)-(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373-2379) are discussed.
References:
-
- 1.
- R. P. Agarwal, Focal Boundary Value Problems for Differential and Difference Equations, Kluwer Academic, Dordrecht, 1998. MR 99h:34036
- 2.
- R. P. Agarwal, D. O'Regan, and P. J. Y. Wong, Positive Solutions of Differential, Difference, and Integral Equations, Kluwer Academic, Dordrecht, 1999. MR 2000a:34046
- 3.
- R. Agarwal and F. H. Wong, Existence of positive solutions for higher order boundary value problems, Nonlinear Studies 5 (1998), 15-24. MR 99e:34024
- 4.
- R. I. Avery, J. M. Davis, and J. Henderson, Three symmetric positive solutions for Lidstone problems by a generalization of the Leggett-Williams theorem, Electron. J. Differential Equations, Vol. 2000 (2000), No. 40, pp 1-15. MR 2001c:34048
- 5.
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- 8.
- P. W. Eloe and J. Henderson, Positive solutions for higher order ordinary differential equations, Electron. J. Differential Equations 1995 (1995), 1-8. MR 96a:34037
- 9.
- L. H. Erbe, S. Hu, and H. Y. Wang, Multiple positive solutions of some boundary value problems, J. Math. Anal. Appl. 184 (1994), 640-648. MR 95f:34023
- 10.
- J. Henderson and H. B. Thompson, Multiple symmetric positive solutions for a second order boundary value problem, Proc. Amer. Math. Soc. 128 (2000), 2373-2379. MR 2000k:34042
- 11.
- M. A. Krasnosel'skii, Positive Solutions of Operator Equations, Noordhoff, Groningen, 1964. MR 31:6107
- 12.
- R. Ma, J. Zhang, and S. Fu, The method of lower and upper solutions for fourth-order two-point boundary value problems, J. Math. Anal. Appl. 215 (1997), 415-422. MR 98i:34037
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Additional Information:
John
R.
Graef
Affiliation:
Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, Tennessee 37403
Email:
john-graef@utc.edu
Chuanxi
Qian
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
Email:
qian@math.msstate.edu
Bo
Yang
Affiliation:
Department of Mathematics and Statistics, Mississippi State University, Mississippi State, Mississippi 39762
Email:
by2@ra.msstate.edu
DOI:
10.1090/S0002-9939-02-06579-6
PII:
S 0002-9939(02)06579-6
Keywords:
Boundary value problems,
existence of positive solutions,
higher order equations,
multiple solutions,
nonlinear equations
Received by editor(s):
April 16, 2001
Received by editor(s) in revised form:
October 2, 2001
Posted:
June 18, 2002
Communicated by:
Carmen C. Chicone
Copyright of article:
Copyright
2002,
American Mathematical Society
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