Abstract
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.
| Original language | English (US) |
|---|---|
| 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.
In: Proceedings of the American Mathematical Society, Vol. 95, No. 1, 1985, p. 70-73.Research output: Contribution to journal › Article
}
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
AN - SCOPUS:84864263679
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 -