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

研究成果: Article査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)5256-5267
ページ数12
ジャーナルNonlinear Analysis, Theory, Methods and Applications
71
11
DOI
出版ステータスPublished - 2009 12 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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