Uniqueness of solutions of nonlinear Dirichlet problems

Wei Ming Ni

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70 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 = 1n2 ∂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.

Original languageEnglish (US)
Pages (from-to)289-304
Number of pages16
JournalJournal of Differential Equations
Volume50
Issue number2
DOIs
StatePublished - Nov 1983

Bibliographical note

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

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