### Abstract

We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ R^{n} is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C^{0}(∈^{̅}) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.

Original language | English (US) |
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Pages (from-to) | 70-73 |

Number of pages | 4 |

Journal | Proceedings of the American Mathematical Society |

Volume | 95 |

Issue number | 1 |

DOIs | |

State | Published - 1985 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**A priori bounds for positive solutions of a semilinear elliptic equation.** / Cosner, George; Schmitt, Klaus.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 95, no. 1, pp. 70-73. https://doi.org/10.1090/S0002-9939-1985-0796444-0

}

TY - JOUR

T1 - A priori bounds for positive solutions of a semilinear elliptic equation

AU - Cosner, George

AU - Schmitt, Klaus

PY - 1985

Y1 - 1985

N2 - We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ Rn is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C0(∈̅) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.

AB - We consider the semilinear elliptic equation -△u = ƒ(u), x ∈ Ω, subject to zero Dirichlet boundary conditions, where ∈ ⊂ Rn is a bounded domain with smooth boundary and the nonlinearity ƒ assumes both positive and negative values. Under the assumption that ∈ satisfies certain symmetry conditions we establish two results providing lower bounds on the C0(∈̅) norm of positive solutions. The bounds derived are the same one obtains in dimension n = 1.

UR - http://www.scopus.com/inward/record.url?scp=84864263679&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864263679&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1985-0796444-0

DO - 10.1090/S0002-9939-1985-0796444-0

M3 - Article

VL - 95

SP - 70

EP - 73

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -