Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity

Adimurthi, ; Grossi, Massimo (2004) Asymptotic estimates for a two-dimensional problem with polynomial nonlinearity Proceedings of the American Mathematical Society, 132 (4). pp. 1013-1019. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/2004-132-04/S0002...

Abstract

In this paper we give asymptotic estimates of the least energy solution up of the functional J(u) =∫Ω|∇u|2 constrained on the manifold ∫Ω|u|p+1= 1 as p goes to infinity. Here Ω is a smooth bounded domain of R2. Among other results we give a positive answer to a question raised by Chen, Ni, and Zhou (2000) by showing that limp→∞||up||=√e.

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Source:Copyright of this article belongs to American Mathematical Society.
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