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Multiple symmetric positive solutions
for a second order boundary value problem

Authors: Johnny Henderson and H. B. Thompson
Journal: Proc. Amer. Math. Soc. 128 (2000), 2373-2379
MSC (2000): Primary 34B15
Published electronically: February 23, 2000
MathSciNet review: 1709753
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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 [Enhancements On Off] (What's this?)

  • [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

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Additional Information

Johnny Henderson
Affiliation: Department of Mathematics, Auburn University, Auburn, Alabama 36849-5310

H. B. Thompson
Affiliation: Centre for Applied Dynamical Systems, Mathematical Analysis and Probability, Department of Mathematics, The University of Queensland, Brisbane, Queensland 4072 Australia

Keywords: Boundary value problem, Green's function, multiple solutions
Received by editor(s): September 19, 1998
Published electronically: February 23, 2000
Communicated by: Hal L. Smith
Article copyright: © Copyright 2000 American Mathematical Society

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