Global bifurcation and positive solution for a class of fully nonlinear problems

Guowei Dai, Haiyan Wang, Bianxia Yang

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

In this paper, we study global bifurcation phenomena for the following Kirchhoff type problem {-M (/ Ω/ ∇u(x)|2 dx) Δu = λf (x, u) in Ω, u = 0 on ∂Ω, where M is a continuous function. Under some natural hypotheses, we show that (λ1(a)M(0), 0) is a bifurcation point and there is a global continuum C emanating from (λ1(a)M(0), 0), where λ1(a) denotes the first eigenvalue of the above problem with f (x, s) = a(x)s. As an application of the above result, we study the existence of positive solution for this problem with asymptotically linear nonlinearity.

Original languageEnglish (US)
Pages (from-to)771-776
Number of pages6
JournalComputers and Mathematics with Applications
Volume69
Issue number8
DOIs
StatePublished - 2015

Keywords

  • Global bifurcation
  • Kirchhoff type problem
  • Positive solution

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Modeling and Simulation
  • Computational Mathematics

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