Uniqueness of solutions of nonlinear Dirichlet problems

Wei Ming Ni

doi:10.1016/0022-0396(83)90079-7

Uniqueness of solutions of nonlinear Dirichlet problems

Wei Ming Ni

Research output: Contribution to journal › Article › peer-review

82 Scopus citations

Abstract

In this paper, we consider the uniqueness of radial solutions of the nonlinear Dirichlet problem Δu + f{hook}(u) = 0 in Ω with u = 0 on ∂Ω, where Δ = ∑_{i = 1}ⁿ ∂² ∂x_i²,f{hook} satisfies some appropriate conditions and Ω is a bounded smooth domain in Rⁿ which possesses radial symmetry. Our uniqueness results apply to, for instance, f{hook}(u) = u^p, p > 1, or more generally λu + ∑_{i = 1}^k a_iu^pi, λ ≥ 0, a_i > 0 and p_i > 1 with appropriate upper bounds, and Ω a ball or an annulus.

Original language	English (US)
Pages (from-to)	289-304
Number of pages	16
Journal	Journal of Differential Equations
Volume	50
Issue number	2
DOIs	https://doi.org/10.1016/0022-0396(83)90079-7
State	Published - Nov 1983
Externally published	Yes

Bibliographical note

Funding Information:
* Supported in part by an NSF grant and a research grant from the Graduate School of the University of Minnesota.

Publisher link

10.1016/0022-0396(83)90079-7

Find It

Find It at U of M Libraries

Cite this

@article{b3e24254e55146c98df43f9fd66f4911,

title = "Uniqueness of solutions of nonlinear Dirichlet problems",

abstract = "In this paper, we consider the uniqueness of radial solutions of the nonlinear Dirichlet problem Δu + f{hook}(u) = 0 in Ω with u = 0 on ∂Ω, where Δ = ∑i = 1n ∂2 ∂xi2,f{hook} satisfies some appropriate conditions and Ω is a bounded smooth domain in Rn which possesses radial symmetry. Our uniqueness results apply to, for instance, f{hook}(u) = up, p > 1, or more generally λu + ∑i = 1k aiupi, λ ≥ 0, ai > 0 and pi > 1 with appropriate upper bounds, and Ω a ball or an annulus.",

author = "Ni, {Wei Ming}",

note = "Funding Information: * Supported in part by an NSF grant and a research grant from the Graduate School of the University of Minnesota.",

year = "1983",

month = nov,

doi = "10.1016/0022-0396(83)90079-7",

language = "English (US)",

volume = "50",

pages = "289--304",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Uniqueness of solutions of nonlinear Dirichlet problems

AU - Ni, Wei Ming

N1 - Funding Information: * Supported in part by an NSF grant and a research grant from the Graduate School of the University of Minnesota.

PY - 1983/11

Y1 - 1983/11

N2 - In this paper, we consider the uniqueness of radial solutions of the nonlinear Dirichlet problem Δu + f{hook}(u) = 0 in Ω with u = 0 on ∂Ω, where Δ = ∑i = 1n ∂2 ∂xi2,f{hook} satisfies some appropriate conditions and Ω is a bounded smooth domain in Rn which possesses radial symmetry. Our uniqueness results apply to, for instance, f{hook}(u) = up, p > 1, or more generally λu + ∑i = 1k aiupi, λ ≥ 0, ai > 0 and pi > 1 with appropriate upper bounds, and Ω a ball or an annulus.

AB - In this paper, we consider the uniqueness of radial solutions of the nonlinear Dirichlet problem Δu + f{hook}(u) = 0 in Ω with u = 0 on ∂Ω, where Δ = ∑i = 1n ∂2 ∂xi2,f{hook} satisfies some appropriate conditions and Ω is a bounded smooth domain in Rn which possesses radial symmetry. Our uniqueness results apply to, for instance, f{hook}(u) = up, p > 1, or more generally λu + ∑i = 1k aiupi, λ ≥ 0, ai > 0 and pi > 1 with appropriate upper bounds, and Ω a ball or an annulus.

UR - http://www.scopus.com/inward/record.url?scp=0001196951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001196951&partnerID=8YFLogxK

U2 - 10.1016/0022-0396(83)90079-7

DO - 10.1016/0022-0396(83)90079-7

M3 - Article

AN - SCOPUS:0001196951

SN - 0022-0396

VL - 50

SP - 289

EP - 304

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Uniqueness of solutions of nonlinear Dirichlet problems

Abstract

Bibliographical note

Publisher link

Find It

Other files and links

Fingerprint

Cite this