Uniqueness of nodal radial solutions superlinear elliptic equations in a ball

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7 Citations (Scopus)

Abstract

The Dirichlet problem is considered, where B = {x ∈ ℝN : |x| < 1}, N ≥ 3, p > 1, K ∈ C2[0, 1] and K(r) > 0 for 0 ≤ r ≤ 1. A sufficient condition is derived for the uniqueness of radial solutions of (*) possessing exactly k - 1 nodes, where k ∈ ℕ. It is also shown that there exists K ∈ C[0, 1] such that (*) has at least three radial solutions possessing exactly k - 1 nodes, in the case 1 < p < (N + 2)/(N - 2).

Original languageEnglish
Pages (from-to)1331-1343
Number of pages13
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume138
Issue number6
DOIs
Publication statusPublished - 2008 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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