An existence theorem for quasilinear systems

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Abstract

This paper deals with the existence of positive radial solutions for the quasilinear system div(|∇ui|p-2ui + λfi (u1,...,un) = 0, |x| < 1, ui(x) = 0, on |x| = 1, i = 1,...,n p > 1, λ > 0, x ∈ ℝN. The fi, i = 1,..., n, are continuous and non-negative functions. Let u = (u1,...,un), ||u|| = Σi=1n |ui|, f0i= lim/||u||→0 fi(u)/||u||p-1 i = 1,..., n, f = (f 1,..., fn), f0 = Σi=1 n f0i. We prove that the problem has a positive solution for sufficiently small λ > 0 if f0 = ∞. Our methods employ a fixed-point theorem in a cone.

Original languageEnglish (US)
Pages (from-to)505-511
Number of pages7
JournalProceedings of the Edinburgh Mathematical Society
Volume49
Issue number2
DOIs
StatePublished - Jun 1 2006

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Keywords

  • Cone
  • Elliptic system
  • Existence
  • Fixed-point theorem
  • p-Laplacian

ASJC Scopus subject areas

  • Mathematics(all)

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