Existence of two non-trivial solutions for a class of quasilinear elliptic variational systems on strip-like domains

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In this paper we study the multiplicity of solutions of the quasilinear elliptic system -Δpu = λFu(x, u, v) in Ω, -Δqv = λFv(x, u, v) in Ω, (Sλ) u = v = 0 on ∂Ω,} where Ω is a strip-like domain and λ > 0 is a parameter. Under some growth conditions on F, we guarantee the existence of an open interval A ⊂ (0, ∞) such that for every λ ∈ Λ, the system (S λ) has at least two distinct, non-trivial solutions. The proof is based on an abstract critical-point result of Ricceri and on the principle of symmetric criticality.

Original languageEnglish
Pages (from-to)465-477
Number of pages13
JournalProceedings of the Edinburgh Mathematical Society
Issue number2
Publication statusPublished - Jun 2005



  • Eigenvalue problem
  • Elliptic systems
  • Principle of symmetric criticality
  • Strip-like domain

ASJC Scopus subject areas

  • Mathematics(all)

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