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Proceedings of the American Mathematical Society

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Existence of positive solutions for
singular ordinary differential equations
with nonlinear boundary conditions

Authors: L. E. Bobisud and Donal O'Regan
Journal: Proc. Amer. Math. Soc. 124 (1996), 2081-2087
MSC (1991): Primary 34B15
MathSciNet review: 1353379
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Abstract: We prove the existence of nonnegative solutions of the problem $(py')'/p+\mu qg(x,y)=0$, $\lim _{x\to 0+}py'=0$, $h(y'(1))+y(1)=0$ for a physically motivated class of nonlinearity $h$. The results, which are established using a ``forbidden value'' argument, are new even in the case of linear $h$.

References [Enhancements On Off] (What's this?)

  • 1. L. E. Bobisud, J. E. Calvert, and W. D. Royalty, Existence of biological populations stabilized by diffusion, Diff. Eqs. Dynamical Systems (to appear).
  • 2. L. H. Erbe and H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994), 743--748. MR 94e:34025
  • 3. A. Granas, R. B. Guenther, and J. W. Lee, Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math. pures et appl. 70 (1991), 153--196. MR 92d:34041
  • 4. D. O'Regan, Theory of singular boundary value problems, World Scientific, Singapore, 1994. MR 95g:34003

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Additional Information

L. E. Bobisud
Affiliation: Department of Mathematics and Statistics, University of Idaho, Moscow, Idaho 83844–1103

Donal O'Regan
Affiliation: Department of Mathematics, University College Galway, Galway, Ireland

Keywords: Boundary value problems, nonlinear boundary conditions, nonlinear alternative
Received by editor(s): January 15, 1995
Communicated by: Hal L. Smith
Article copyright: © Copyright 1996 American Mathematical Society

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