### Abstract

Assume that Ω is a bounded domain in R
^{n}
with n ≥ 2. We study positive solutions to the problem, ∆u = u
^{p}
in Ω, u(x) → ∞ as x → ∂Ω, where p > 1. Such solutions are called boundary blow-up solutions of ∆u = u
^{p}
. We show that a boundary blow-up solution exists in any bounded domain if 1 < p (Formula presented). In particular, when n = 2, there exists a boundary blow-up solution to ∆u = u
^{p}
for all p ∈ (1, ∞). We also prove the uniqueness under the additional assumption that the domain satisfies the condition ∂Ω = ∂Ω.

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

Pages (from-to) | 245-251 |

Number of pages | 7 |

Journal | Bulletin of the Korean Mathematical Society |

Volume | 56 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2019 Jan 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

}

^{p}',

*Bulletin of the Korean Mathematical Society*, vol. 56, no. 1, pp. 245-251. https://doi.org/10.4134/BKMS.b180221

**
A note on boundary blow-up problem of ∆u = u
^{p}
.** / Kim, Seick.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A note on boundary blow-up problem of ∆u = u p

AU - Kim, Seick

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Assume that Ω is a bounded domain in R n with n ≥ 2. We study positive solutions to the problem, ∆u = u p in Ω, u(x) → ∞ as x → ∂Ω, where p > 1. Such solutions are called boundary blow-up solutions of ∆u = u p . We show that a boundary blow-up solution exists in any bounded domain if 1 < p (Formula presented). In particular, when n = 2, there exists a boundary blow-up solution to ∆u = u p for all p ∈ (1, ∞). We also prove the uniqueness under the additional assumption that the domain satisfies the condition ∂Ω = ∂Ω.

AB - Assume that Ω is a bounded domain in R n with n ≥ 2. We study positive solutions to the problem, ∆u = u p in Ω, u(x) → ∞ as x → ∂Ω, where p > 1. Such solutions are called boundary blow-up solutions of ∆u = u p . We show that a boundary blow-up solution exists in any bounded domain if 1 < p (Formula presented). In particular, when n = 2, there exists a boundary blow-up solution to ∆u = u p for all p ∈ (1, ∞). We also prove the uniqueness under the additional assumption that the domain satisfies the condition ∂Ω = ∂Ω.

UR - http://www.scopus.com/inward/record.url?scp=85062337624&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062337624&partnerID=8YFLogxK

U2 - 10.4134/BKMS.b180221

DO - 10.4134/BKMS.b180221

M3 - Article

AN - SCOPUS:85062337624

VL - 56

SP - 245

EP - 251

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

SN - 1015-8634

IS - 1

ER -