### 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 language | English (US) |
---|---|

Pages (from-to) | 771-776 |

Number of pages | 6 |

Journal | Computers and Mathematics with Applications |

Volume | 69 |

Issue number | 8 |

DOIs | |

State | Published - 2015 |

### Keywords

- Global bifurcation
- Kirchhoff type problem
- Positive solution

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Modeling and Simulation
- Computational Mathematics

## Fingerprint Dive into the research topics of 'Global bifurcation and positive solution for a class of fully nonlinear problems'. Together they form a unique fingerprint.

## Cite this

Dai, G., Wang, H., & Yang, B. (2015). Global bifurcation and positive solution for a class of fully nonlinear problems.

*Computers and Mathematics with Applications*,*69*(8), 771-776. https://doi.org/10.1016/j.camwa.2015.02.020