EXISTENCE OF TWO NON-TRIVIAL SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC VARIATIONAL SYSTEMS ON STRIP-LIKE DOMAINS

Abstract In this paper we study the multiplicity of solutions of the quasilinear elliptic system −∆pu = λFu(x, u, v) in Ω, −∆qv = λFv(x, u, v) in Ω, u = v = 0 on ∂Ω, ⎪ ⎭ (Sλ) 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 Λ ⊂ (0,∞) such that for every λ ∈ Λ, the system (Sλ) 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