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

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Abstract

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

Original languageEnglish
Pages (from-to)259-263
Number of pages5
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume97
DOIs
Publication statusPublished - 1 Jan 1984

ASJC Scopus subject areas

  • Mathematics(all)

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