### Abstract

We investigate the existence of positive principal eigenvalues of the problem − Δu(x) = λg(x)u for x ϵ R^{n}; u(x) → 0 as x → ∞ where the weight function g changes sign on R^{n}. It is proved that such eigenvalues exist if g is negative and bounded away from 0 at ∞ or if n ≥ 3 and |g(x)| is sufficiently small at ∞ but do not exist if n = 1 or 2.

Original language | English (US) |
---|---|

Pages (from-to) | 147-155 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 109 |

Issue number | 1 |

DOIs | |

State | Published - 1990 |

### Fingerprint

### Keywords

- Elliptic boundary value problems
- Indefinite weight function
- Spectral theory

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

^{n}

*Proceedings of the American Mathematical Society*,

*109*(1), 147-155. https://doi.org/10.1090/S0002-9939-1990-1007489-1

**Principal eigenvalues for problems with indefinite weight function on r ^{n} .** / Brown, K. J.; Cosner, George; Fleckinger, J.

Research output: Contribution to journal › Article

^{n}',

*Proceedings of the American Mathematical Society*, vol. 109, no. 1, pp. 147-155. https://doi.org/10.1090/S0002-9939-1990-1007489-1

^{n}Proceedings of the American Mathematical Society. 1990;109(1):147-155. https://doi.org/10.1090/S0002-9939-1990-1007489-1

}

TY - JOUR

T1 - Principal eigenvalues for problems with indefinite weight function on rn

AU - Brown, K. J.

AU - Cosner, George

AU - Fleckinger, J.

PY - 1990

Y1 - 1990

N2 - We investigate the existence of positive principal eigenvalues of the problem − Δu(x) = λg(x)u for x ϵ Rn; u(x) → 0 as x → ∞ where the weight function g changes sign on Rn. It is proved that such eigenvalues exist if g is negative and bounded away from 0 at ∞ or if n ≥ 3 and |g(x)| is sufficiently small at ∞ but do not exist if n = 1 or 2.

AB - We investigate the existence of positive principal eigenvalues of the problem − Δu(x) = λg(x)u for x ϵ Rn; u(x) → 0 as x → ∞ where the weight function g changes sign on Rn. It is proved that such eigenvalues exist if g is negative and bounded away from 0 at ∞ or if n ≥ 3 and |g(x)| is sufficiently small at ∞ but do not exist if n = 1 or 2.

KW - Elliptic boundary value problems

KW - Indefinite weight function

KW - Spectral theory

UR - http://www.scopus.com/inward/record.url?scp=84966229474&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966229474&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1990-1007489-1

DO - 10.1090/S0002-9939-1990-1007489-1

M3 - Article

VL - 109

SP - 147

EP - 155

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -