Existence of multiple positive solutions of semilinear elliptic boundary value problems in the half space

Tsing San Hsu*, Huei Li Lin

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

3 Scopus citations

Abstract

In this paper, we prove that if Q and f satisfy some suitable conditions, then - Δ u + u = Q (x) f (u) in R+N with the boundary condition u (y, 0) = λ g (y) has at least two positive solutions if 0 < λ < λ*, a unique positive solution if λ = λ* and no positive solution if λ > λ*.

Original languageEnglish
Pages (from-to)849-865
Number of pages17
JournalNonlinear Analysis, Theory, Methods and Applications
Volume70
Issue number2
DOIs
StatePublished - 15 01 2009

Keywords

  • Boundary value problems
  • Multiple positive solutions
  • Semilinear elliptic
  • The half space

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