Uniqueness and nonuniqueness of nodal radial solutions of sublinear elliptic equations in a ball

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8 Citations (Scopus)

Abstract

The following Dirichlet problem (1.1){(Δ u + K (| x |) f (u) = 0, in B,; u = 0, on ∂ B,) is considered, where B = {x ∈ RN : | x | < 1}, N ≥ 2, K ∈ C2 [0, 1] and K (r) > 0 for 0 ≤ r ≤ 1, f ∈ C1 (R), s f (s) > 0 for s ≠ 0. Assume moreover that f satisfies the following sublinear condition: f (s) / s > f (s) for s ≠ 0. A sufficient condition is derived for the uniqueness of radial solutions of (1.1) possessing exactly k - 1 nodes, where k ∈ N. It is also shown that there exists K ∈ C [0, 1] such that (1.1) has three radial solutions having exactly one node in the case N = 3.

Original languageEnglish
Pages (from-to)5256-5267
Number of pages12
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number11
DOIs
Publication statusPublished - 2009 Dec 1
Externally publishedYes

Keywords

  • Elliptic equation
  • Nodal solution
  • Radial solution
  • Sublinear

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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