Non‐existence results for an eigenvalue problem involving Lipschitzian non‐linearities with non‐positive primitive. Issue 3 (8th April 2019)

• Record Type: Journal Article
• Authors: Goubet, Olivier; Ricceri, Biagio
• Is Part Of: Bulletin of the London Mathematical Society. Volume 51:Issue 3(2019)
• Page Start: 531
• Page End: 538
• Publication Date: 2019-04-08
• Subjects: 35J61 (primary) -- 35P30 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12249
• Languages: English
• ISSNs: 0024-6093

Abstract

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 that sup ξ ∈ R ∫ 0 ξ f ( t ) d t = 0, the problem − Δ u = f ( u ) in Ω, u = 0 on ∂ Ω has no non‐zero classical solutions.