In this paper we construct families of bounded domains Ωε and solutions uε of (Formula presented ) such that, for any integer k ≥ 2, uε admits at least k maximum points for small enough ɛ. The domain Ωε is “not far” to be convex in the sense that it is starshaped, the curvature of ∂Ωε vanishes at exactly two points and the minimum of the curvature of ∂Ωε goes to 0 as ε → 0.
ON THE NUMBER OF CRITICAL POINTS OF SOLUTIONS OF SEMILINEAR EQUATIONS IN R2 / Gladiali, F.; Grossi, M.. - In: AMERICAN JOURNAL OF MATHEMATICS. - ISSN 0002-9327. - 144:5(2022), pp. 1221-1240. [10.1353/ajm.2022.0028]
ON THE NUMBER OF CRITICAL POINTS OF SOLUTIONS OF SEMILINEAR EQUATIONS IN R2
Gladiali F.;
2022-01-01
Abstract
In this paper we construct families of bounded domains Ωε and solutions uε of (Formula presented ) such that, for any integer k ≥ 2, uε admits at least k maximum points for small enough ɛ. The domain Ωε is “not far” to be convex in the sense that it is starshaped, the curvature of ∂Ωε vanishes at exactly two points and the minimum of the curvature of ∂Ωε goes to 0 as ε → 0.File in questo prodotto:
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