Available in electronic format
Available in print format		 Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Multiple symmetric positive solutions for a second order boundary value problem

Author(s): Johnny Henderson; H. B. Thompson
Journal: Proc. Amer. Math. Soc. 128 (2000), 2373-2379.
MSC (2000): Primary 34B15
Posted: February 23, 2000
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: For the second order boundary value problem, $y''+f(y)=0$, $0\leq t\leq 1$, $y(0)=0=y(1)$, where $f:\, \mathbb{R}\rightarrow [0,\,\infty),$ growth conditions are imposed on $f$ which yield the existence of at least three symmetric positive solutions.

References:

[1]
D. Anderson, Multiple positive solutions for a three-point boundary value problem, Mathematical and Computer Modelling 27 (1998), 49-57. MR 99b:34040

[2]
R. Avery, Existence of multiple positive solutions to a conjugate boundary value problem, MSR Hot-Line, 2, No.1 (1998), 1-6. MR 98i:34034

[3]
R. Avery and A. Peterson, Multiple positive solutions of a discrete second order conjugate problem, Pan American Mathematical Journal, 8 (1998), 1-12. MR 99i:39001

[4]
D. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Boston, 1988. MR 89k:47084

[5]
J. Henderson and H.B. Thompson, Existence of multiple solutions for some $n$-th order boundary value problems, preprint.

[6]
R. Leggett and L. Williams, Multiple positive fixed points of nonlinear operators on ordered Banach spaces, Indiana University Mathematics Journal, 28 (1979), 673-688. MR 80i:47073

[7]
Y. Sun and J.-X. Sun, Multiple positive fixed points of weakly inward mappings, Journal of Mathematical Analysis and Applications, 148 (1990), 431-439. MR 91f:47084

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 34B15

Retrieve articles in all Journals with MSC (2000): 34B15

Additional Information:

Johnny Henderson
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849-531
Email: hendej2@mail.auburn.edu

H. B. Thompson
Affiliation: Centre for Applied Dynamical Systems, Mathematical Analysis and Probability, Department of Mathematics, The University of Queensland, Brisbane, Queensland 4072 Australia
Email: hbt@maths.uq.edu.au

DOI: 10.1090/S0002-9939-00-05644-6
PII: S 0002-9939(00)05644-6
Keywords: Boundary value problem, Green's function, multiple solutions
Received by editor(s): September 19, 1998
Posted: February 23, 2000
Communicated by: Hal L. Smith
Copyright of article: Copyright 2000, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google