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Uniqueness of positive solutions of some semilinear Sturm–Liouville problems on the half line

Published online by Cambridge University Press:  14 November 2011

J. F. Toland
J. F. Toland
Affiliation:
School of Mathematics, University of Bath, Claverton Down, Bath BA2 7AY
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Synopsis

This note gives a simple proof of uniqueness for positive solutions of certain non-linear boundary value problems on ℝ+ which are typified by the equation

with boundary conditions u′(0) = u(+∞) = 0. In the autonomous case (r ≡ 1), this is easy to see, by quadrature. The proof here supposes r to be non-increasing on ℝ+.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 97 , 1984 , pp. 259 - 263
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Peletier, L. A. and Serrin, J.. Uniqueness of positive solutions of semilinear equations in ℝN. Arch. Rational Mech. Anal. 81 (1983), 181–197.Google Scholar
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3Toland, J. F.. Global bifurcation for Neumann problems without eigenvalues. J. Differential Equations 44 (1982), 82–110.Google Scholar