### Abstract

The degenerate elliptic equation λΔ_{p}u + uq–1(1 – u^{r}) = 0 with zero Dirichlet boundary condition, where λ is a positive parameter, 2 p q and r 0, is studied in three aspects: existence of maximal solution, λ dependence of maximal solution and multiplicity of solutions.

Original language | English |
---|---|

Pages (from-to) | 433-441 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 129 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2000 |

Externally published | Yes |

### Fingerprint

### Keywords

- At core
- At hat
- Degenerate elliptic equation
- Multiple solutions
- P-Laplace operator

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Positive solutions of a degenerate elliptic equation with logistic reaction.** / Takeuchi, Shingo.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Positive solutions of a degenerate elliptic equation with logistic reaction

AU - Takeuchi, Shingo

PY - 2000

Y1 - 2000

N2 - The degenerate elliptic equation λΔpu + uq–1(1 – ur) = 0 with zero Dirichlet boundary condition, where λ is a positive parameter, 2 p q and r 0, is studied in three aspects: existence of maximal solution, λ dependence of maximal solution and multiplicity of solutions.

AB - The degenerate elliptic equation λΔpu + uq–1(1 – ur) = 0 with zero Dirichlet boundary condition, where λ is a positive parameter, 2 p q and r 0, is studied in three aspects: existence of maximal solution, λ dependence of maximal solution and multiplicity of solutions.

KW - At core

KW - At hat

KW - Degenerate elliptic equation

KW - Multiple solutions

KW - P-Laplace operator

UR - http://www.scopus.com/inward/record.url?scp=85009726553&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009726553&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-00-05723-3

DO - 10.1090/S0002-9939-00-05723-3

M3 - Article

AN - SCOPUS:85009726553

VL - 129

SP - 433

EP - 441

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -