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.
- Eigenvalue problem
- Elliptic systems
- Principle of symmetric criticality
- Strip-like domain
ASJC Scopus subject areas