On the number of positive solutions of nonlinear systems

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Abstract

We prove that appropriate combinations of superlinearity and sublinearity of f(u) with respect to Φ at zero and infinity guarantee the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system (Φ(u′) ′ + λh(t)f(u) = 0, 0 < t < 1. The vector-valued function Φ is defined by Φ(u′) = ( (u1′ ,..., (un′)), where u = (u1,...,un and covers the two important cases (u′) = u′ and (u′) = u′ p-2u′, p > 1. Our methods employ fixed point theorems in a cone.

Original languageEnglish (US)
Pages (from-to)287-306
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume281
Issue number1
DOIs
StatePublished - May 1 2003

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ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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