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Non‐existence results for an eigenvalue problem involving Lipschitzian non‐linearities with non‐positive primitive
Author(s) -
Goubet Olivier,
Ricceri Biagio
Publication year - 2019
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12249
Subject(s) - mathematics , bounded function , annulus (botany) , eigenvalues and eigenvectors , zero (linguistics) , domain (mathematical analysis) , pure mathematics , curvature , function (biology) , mean curvature , combinatorics , mathematical analysis , geometry , quantum mechanics , linguistics , philosophy , botany , physics , evolutionary biology , biology
Abstract Let Ω ⊂ R N( N ⩾ 2 ) be a bounded smooth domain. In this paper, we prove that if either ∂ Ω has non‐negative mean curvature or Ω is an annulus, then, for each Lipschitzian function f : R → R such thatsup ξ ∈ R∫ 0 ξ f ( t ) d t = 0 , the problem− Δ u=f ( u )inΩ ,u =0on∂ Ωhas no non‐zero classical solutions.