Four positive solutions for the semilinear elliptic equation: - Δu + u = a(x)up + f(x) in ℝN

Shinji Adachi, Kazunaga Tanaka

研究成果: Article査読

86 被引用数 (Scopus)

抄録

We consider the existence of positive solutions of the following semilinear elliptic problem in ℝN: (Formula Presented) where 1 < p < N + 2/N - 2 (N ≥ 3), 1 < p < ∞ (N = 1, 2), a(x) ∈ C(ℝN), f(x) ∈ H-1 (ℝN) and f(x) ≥ 0. Under the conditions: 1° a(x) ∈ (0, 1) for all x ∈ ℝN, 2° a(x) → 1 as |x| → ∞, 3° there exist δ > 0 and C > 0 such that a(x) - 1 ≥ -Ce-(2+δ)|x| for all x ∈ ℝN, 4° a(x) ≢ 1, we show that (*) has at least four positive solutions for sufficiently small ||f||H-1(ℝN) but f ≢ 0.

本文言語English
ページ(範囲)63-95
ページ数33
ジャーナルCalculus of Variations and Partial Differential Equations
11
1
DOI
出版ステータスPublished - 2000 8

ASJC Scopus subject areas

  • 分析
  • 応用数学

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