Solutions of semilinear elliptic equations with asymptotic linear nonlinearity

Cheng Hsiung Hsu, Yi Wen Shih

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The existence, uniqueness and asymptotic behavior of positive solutions of the semilinear elliptic equations with asymptotic linear nonlinearity was studied. It was proved that if ε > 0, then there existed exactly one solution uλ(.,ε) for all λ ∈ (0,λ1) where λ1 represents first eignvalue of -δ in ω with Dirichlet boundary condition. The results showed that if s < t and small enough, δū+λfε(ū) < -s + ||h(ū)|| ≤ 0 was found by choosing δ = s.

Original languageEnglish
Pages (from-to)275-283
Number of pages9
JournalNonlinear Analysis, Theory, Methods and Applications
Volume50
Issue number2
DOIs
StatePublished - Jul 2002

Keywords

  • Hopf lemma
  • Minimal solution
  • Perturbation lemma
  • Variation method of Nehari-type

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